Drilling energy calculation based on transient dynamics simulation and its application to drilling optimization

A method for drilling a well includes applying energy input to a drill string (31) by at least one of rotating the drill string (31) from surface and operating a drilling motor (41) disposed in the drill string (31) to operate a drill bit (2) at a bottom of the drill string (31); an amount of the applied energy not consumed in drilling formations caused by at least one of motion, deformation, and interaction of the drill string (31) is calculated; an amount of the applied energy used to drill formations below the drill bit (2) is calculated; and at least one drilling operating parameter is adjusted based on energy calculation before or during drilling operation.

BACKGROUND

This disclosure relates generally to the field of drilling subsurface wellbores. More specifically, the disclosure relates to methods and apparatus for determining an amount of energy used to turn a drill string and/or sections thereof that is communicated to a drill bit used to drill through subsurface formations. Calculations of energy loss may be used to aid drilling job planning, drilling job execution and drilling job post evaluation.

Drilling is a process in which supplied energy and gravity act on a drill string from the surface, and/or by certain types of drilling motors coupled within the drill string. The energy is transferred through drill string, and is used to cut the formations at the bottom of the wellbore to extend its length. Part of the energy input may be converted to drill string elastic strain/kinetic energy; other portions of the input energy may be dissipated as thermal energy generated by frictional torque and axial drag between the drill string and the wall of the wellbore.

From an energy point of view, drilling optimization is a process used to minimize the energy loss due to drilling dynamics and to make as full use as practical of the energy input to the drill string to drill the formations.

Drilling energy analysis methods known in the art include, for example, “Vybs” bottom hole assembly (BHA) analysis model and energy-based performance indices. Descriptions of the foregoing may be found in Transactions of the International Petroleum Technology Conference (IPTC) Paper No., 12737-MS entitled,Development and Application of a BHA Vibrations Model. Other references include Society of Petroleum Engineers International (SPE) Paper No. 112650, Drilling Vibrations Modeling and Field Validation, and Paper No. 139426, entitled,Managing Drilling Vibrations Through BHA Design Optimization.

The methods described in the foregoing two SPE papers are based on a lumped-parameter model using the state vectors and transfer-function matrices. The state vector is a complete description of BHA response at any given position at given time. The total system response includes a static solution plus a dynamic perturbation about the static equilibrium state. In the foregoing described methods, the response of only the BHA section and one stand of heavy weight drill pipe (HWDP) are simulated. Two vibration excitation modes are utilized in the described methods: (1) flex mode wherein harmonic side force is applied at the drill bit, and the frequency is 1×, 2×, or 3× of input bit RPM, and (2) twirl mode, wherein identical mass eccentricity is applied at each model element. The performance parameters generated by such methods include:BHA performance indices developed in the model;BHA bending strain energy;Transmitted bending strain energy;Curvature index of BHA top-point; andContact force index.

U.S. Patent Application Publication No. 2014/0129148 entitled, Downhole determination of drilling state discloses using downhole measurements made by sensors in certain components of the BHA (accelerometer, magnetometer, and strain gauge) to calculate BHA strain and kinetic energy terms as follows:Energy of axial motion and deformation;Energy of rotational motion and deformation;Energy of lateral motion and bending deformation; and whereinthe total energy per unit length of BHA is obtained by summing the energy terms in different directions, and the foregoing terms can be used to detect changes in the operating state of the drill string and/or BHA automatically.

SUMMARY

One aspect of the disclosure relates to a method for drilling a well. A method according to this aspect of the disclosure includes applying energy to a drill string at at least one of a surface of the drill string and a motor disposed in the drill string to drive a drill bit at a bottom of the drill string. An amount of the applied energy not consumed in drilling formations caused by deformation and motion of the drill string is calculated. An amount of the applied energy used to drill formations below the drill bit is calculated. At least one of the bit, a bottom hole assembly component, and at least one drilling operating parameter is selected or adjusted based on energy calculation before or during drilling operation.

Other aspects and advantages of methods according to the disclosure will be apparent from the description and claims which follow.

DETAILED DESCRIPTION

InFIG. 1, a drilling unit or “drilling rig” is designated generally at11. The drilling rig11inFIG. 1is shown as a land-based drilling rig. However, as will be apparent to those skilled in the art, the examples described herein will find equal application on marine drilling rigs, such as jack-up rigs, semisubmersibles, drill ships, and the like.

The drilling rig11includes a derrick13that is supported on the ground above a rig floor15. The drilling rig11includes lifting gear, which includes a crown block17mounted to derrick13and a traveling block19. The crown block17and the traveling block19are interconnected by a cable21that is driven by draw works23to control the upward and downward movement of the traveling block19. The draw works23may be configured to be automatically operated to control rate of drop or release of the drill string into the wellbore during drilling. One non-limiting example of an automated draw works release control system is described in U.S. Pat. No. 7,059,427 issued to Power et al. and incorporated herein by reference.

The traveling block19carries a hook25from which may be suspended a top drive27. The top drive27supports a drill string, designated generally by the numeral31, in a wellbore33. According to an example implementation, the drill string31may in signal communication with and mechanically coupled to the top drive27through an instrumented sub29. As will be described in more detail, the instrumented top sub29may include sensors (not shown separately) that provide drill string torque information. Other types of torque sensors may be used in other examples, or proxy measurements for torque applied to the drill string31by the top drive27may be used, non-limiting examples of which may include electric current or hydraulic fluid flow drawn by a motor (not shown) in the top drive. A longitudinal end of the drill string31includes a drill bit2mounted thereon to drill the formations to extend (drill) the wellbore33.

The top drive27can be operated to rotate the drill string31in either direction, as will be further explained. A load sensor26may be coupled to the hook25in order to measure the weight load on the hook25. Such weight load may be related to the weight of the drill string31, friction between the drill string31and the wellbore33wall and an amount of the weight of the drill string31that is applied to the drill bit2to drill the formations to extend the wellbore33.

The drill string31may include a plurality of interconnected sections of drill pipe35a bottom hole assembly (BHA)37, which may include stabilizers, drill collars, and a suite of measurement while drilling (MWD) and or logging while drilling (LWD) instruments, shown generally at51.

A steerable drilling motor41may be connected proximate the bottom of BHA37. The steerable drilling motor41may be any type known in the art for rotating the drill bit2and/or selected portions of the drill string31and to enable change in trajectory of the wellbore during slide drilling (explained in the Background section herein) or to perform rotary drilling (also explained in the Background section herein). Example types of drilling motors include, without limitation, positive displacement fluid operated motors, turbine fluid operated motors, electric motors and hydraulic fluid operated motors. The present example steerable drilling motor41may be operated by drilling fluid flow. Drilling fluid may be delivered to the drill string31by mud pumps43through a mud hose45. In some examples, pressure of the drilling mud may be measured by a pressure sensor49. During drilling, the drill string31is rotated within the wellbore33by the top drive27, in a manner to be explained further below. As is known in the art, the top drive27is slidingly mounted on parallel vertically extending rails (not shown) to resist rotation as torque is applied to the drill string31. During drilling, the bit2may be rotated by the steerable drilling motor41, which in the present example may be operated by the flow of drilling fluid supplied by the mud pumps43. Although a top drive rig is illustrated, those skilled in the art will recognize that the present example embodiment may also be used in connection with drilling systems in which a rotary table and kelly are used to apply torque to the drill string31at the surface. Drill cuttings produced as the bit2drills into the subsurface formations to extend the wellbore33are carried out of the wellbore33by the drilling mud as it passes through nozzles, jets or courses (none shown) in the drill bit2. Although a steerable motor is shown inFIG. 1, in some embodiments, no drilling motor may be used, or a “straight” motor (one that is not intended to alter the wellbore trajectory) may be used to equal effect.

Signals from the pressure sensor49, the hookload sensor26, the instrumented top sub29and from an MWD/LWD system or steering tool51(which may be communicated using any known wellbore to surface communication system), may be received in a control unit48. The control unit48may have a general purpose programmable computer (not shown separately) or may communicate with a different computer or computer system located remotely from the drilling rig11for data processing as will be further explained below.

In operating the drilling system shown inFIG. 1, certain operating parameters may be controlled by the drilling system operator (the driller). Such parameters include the hookload, the drill string RPM applied at surface, whether by the top drive as illustrated or by a rotary table. The drilling rig mud pump flow rate may also be controlled by the driller. If a directional drilling motor is used, the “toolface” angle (direction of a bend in the housing of such motor) may also be controlled by the driller. The foregoing may be referred to as “drilling operating parameters.” The response of the drill string (including various modes of vibration) and the drill bit in drilling formations may be referred to as “drilling response parameters.” In some embodiments, as will be further explained, one or more drilling operating parameters may be adjusted by the driller in order to optimize the amount of applied energy that is consumed by drilling formations, while minimizing the amount of energy dissipated in drill string actions that do not transfer energy to drilling the formations.

While the example embodiment of a drilling system shown inFIG. 1applies energy to the drill string in the form of rotational energy (whether by rotating the drill string at the surface and/or operating a rotary-type drilling motor disposed in the drill string, methods according to the present disclosure are not limited to applying and using rotational energy in the drill string and/or drill bit. Other types of drilling systems and drill bits include, for example, and without limitation, percussion bits and percussion motors. A non-limiting example of an hydraulically powered percussion motor and associated drill bit are disclosed in U.S. Pat. No. 4,958,960 issued to Cyphelly.

Having explained a drilling system that may be used in some embodiments, methods according to the present disclosure that may be used to calculate: (i) an amount of the input energy that is actually expended in drilling through formations; and (ii) the amount of the total energy input is dissipated in various modes which do not contribute to extension of the wellbore.

Consider the drill string as a dynamic system. System energy input may be from a surface top drive (or kelly/rotary table as explained with reference toFIG. 1) and/or a drilling motor disposed in the drill string. Effective use of the input energy is to drill and remove the formation (i.e., lengthening the wellbore). However, some of all of the input energy may be dissipated due to shock, vibration and frictional contact between the drill string and the wall of the wellbore. The purpose of drilling optimization according to the present disclosure is to minimize the energy loss caused by, e.g., and without limitation the foregoing interactions of the drill string. The foregoing is illustrated schematically inFIG. 2Ain the general sense.FIG. 2Bshows a schematic illustration of the various interactions between the drill string and the wellbore to better define the parameters which cause loss of energy applied to the drill string that would ideally be used to drill the formations. The input energy to the entire drill string is shown at the rig (top drive or rotary table). Additional energy may be input proximate the BHA using a drilling motor as shown inFIG. 2B. Sources of energy consumption include drilling the formations, indicated by Bit/Rock interaction inFIG. 2B. Energy losses, i.e., energy not used in drilling the formation may result from Elastic strain energy (ε, σ) due to bending moment, torque, and axial force, contact between the wall of the wellbore and the drill string (which may cause both rotational and longitudinal friction). Kinetic energy of axial motion of the drill string (FIG. 3), rotation of the drill string (FIG. 4), tilt motion of the drill string (FIG. 5) and lateral motion of the drill string (FIG. 3).

In a method according to the present disclosure, the entire drill string may be “meshed” into a finite element analysis (FEA) program of types well known in the art. The mesh size is a matter of discretion for the system user or designer and may be selected to provide results to a size range consistent with the user's or designer's objectives. One example of such program as applied to dynamic drill string analysis is disclosed in U.S. Pat. No. 7,139,689 issued to Huang and incorporated herein by reference.

First, the energy that is input to the drill string may be calculated based on hookload (suspended drill string weight in the drilling rig), on torque applied by the top drive (or rotary table) and torque applied by the drilling motor (if used).

The work (energy input) done by top drive or rotary table torque (STOR) may be defined by the expression”
WSTOR=∫STOR·d(REVtable)  (1)
wherein REVtablerepresents the surface rotation revolution imparted to the drill string.

The work by hookload may be defined as:
WHL=−∫HookLoad·d(MD)  (2)
wherein MD is the measured depth of drill string, and the negative sign indicates that the direction of increased measured depth is opposite to the direction of hookload.

The work by net drill string weight may be represented by:
WWT=∫[∫WTDS(x)·cos(Inc(x))·dx]·d(MD)  (3)

where WTDS(x) is the wet weight distribution of drill string versus the distance x, Inc(x) is the inclination of drill string from vertical versus the distance x. The surface weight on bit (SWOB) may be determined by the expression:
SWOB=∫WTDS(x)·cos(Inc(x))·dx−HookLoad  (4)
The total energy applied to the drill string from the surface may be expressed as:
Winput=WSTOR+WHL+WWT=∫STOR·d(REVtable)+∫SWOB·d(MD)  (5)

If a drilling motor is used, its energy applied to that portion of the drill string below the axial position of the drilling motor, in the case of a positive displacement motor, may be calculated by the expression:
Winput_PDM=∫Pdiff·dQ(6)
wherein Pdiffis the pressure drop cross the motor, and Q the flow volume passing the motor. Corresponding expressions for energy input from a drilling motor that is a turbine type are known in the art. When both surface rotation of the drill string and a motor are used, the total energy applied to the drill string will be the sum of Eqs. (5) and (6).

It will be appreciated that by using FEA transient dynamics simulation, each discrete time interval will have the foregoing parameters calculated; the integral sign is intended to represent that the total energy is the sum of the energy generated within each discrete time interval in transient dynamics simulation. From the transient dynamics simulation, the axial displacement, rotational revolution of top node (representing surface), surface weight-on-bit, and surface torque at the discrete time point tnare output and represented by uxtop(tn), REVtable(tn), SWOB(tn), and STOR(tn) respectively. One can calculate the surface energy input to drill string using the classic trapezoidal numerical integration method.

Winput⁡(tN)=∑i=1⁢…⁢⁢N⁢[SWOB⁡(ti)+SWOB⁡(ti-1)]·⌊uxtop⁡(ti)-uxtop⁡(ti-1)⌋2+∑i=1⁢…⁢⁢N⁢[STOR⁡(ti)+STOR⁡(ti-1)]·[REVtop⁡(ti)-REvtop⁡(ti-1)]2(7)Here, Winput(tN) is the surface energy input at time tN. Following the same procedure, one can calculate the motor input to drill string as:

Wi⁢nput⁢_⁢PDM⁡(tN)=∑i=1⁢…⁢⁢N⁢⌊Pdiff⁡(ti)+Pdiff⁡(ti-1)⌋·[Q⁡(ti)-Q⁡(ti-1)]2(8)
Here, Winput_PDM(tn), Pdiff(tn), and Q(tn) are motor energy input, motor differential pressure, and flow volume at time tn.

Once the total energy applied to the drill string is calculated, various parameters that consume energy (including that used in drilling formations) may be calculated so as to enable determining how the input energy is distributed.

Reaction axial force at the drill bit (DWOB) and torque at the drill bit (DTOB) are generated as bit cuts the rock. Energy used by drilling formations equals to the work done by the DWOB and DTOB as in the following expression:
Wdrilling=∫DWOB·d(MDbit)+∫DTOB·d(REVbit)  (9)
wherein REVbitis the rotation revolution of bit, and MDbitis the axial drill ahead distance at bit. The integration can be also evaluated using the trapezoidal numerical integration method based on the transient dynamics simulation outputs.

Wdrilling⁡(tN)=∑i=1⁢…⁢⁢N⁢[DWOB⁡(ti)+DWOB⁡(ti-1)]·[uxbit⁡(ti)-uxbit⁡(ti-1)]2+∑i=1⁢…⁢⁢N⁢[DTOB⁡(ti)+DTOB⁡(ti-1)]·[REVbit⁡(ti)-REVbit⁡(ti-1)]2(10)
wherein Wdrilling(tn), DWOB(tn), DTOB(tn), uxbit(tn), and REVbit(tn) are rock drilling energy, axial force on bit, torque on bit, bit axial displacement, and bit rotational revolution at time tnrespectively.

The strain energy is mechanical energy stored in an elastic material upon deformation caused by mechanical loading. The strain energy may be expressed as:
UStrain=½∫εσdV(11)

For a drill string, the strain energy can be decomposed into three parts: (i) torsional strain energy resulting from torque; (ii) bending strain energy caused by bending moment; (iii) tensile strain energy caused by axial force. The shear strain (energy) due to shear force is negligible as predicted by the Euler-Bernoulli theory. Consider a beam with uniform cross section. The foregoing strain energy components may be calculated according to the respective formulas shown inFIG. 6. For axial loading, the strain energy may be calculated by the expression:

USE⁢_⁢Axial=P2⁢L2⁢⁢AE(12)
wherein P is axial force, L the beam length, A the cross section area, and E is elastic modulus.
Torsional strain energy may be calculated by the expression:

USE⁢_⁢Tor=T2⁢L2⁢⁢GIx(13)
wherein T is the externally applied torque, G the shear modulus, and Ixthe area moment of inertia about the beam axis.
and bending strain energy may be calculated by the expression:

USE⁢_⁢Bending=M2⁢L2⁢⁢EIyz(14)
Wherein M is the applied bending moment, and Iyzis the bending moment of inertia.
In numerical method (FEA) mentioned in this disclosure, the drill string is meshed using beam elements. For each beam element, the foregoing strain energy parameters are calculated using Eq. (12-14). The total strain energy of drill string are the sum of strain energy of each mesh element.

UStraint⁡(tN)=∑i=all⁢⁢ele⁢[Pi⁡(tN)2⁢Li2⁢Ai⁢E+Ti⁡(tN)2⁢Li2⁢Ix,i⁢G+Mi⁡(tN)2⁢Li2⁢Iyz,i⁢E](15)
Here, Ustrain(tN) is the total strain energy at time tN. Pi(tN), Ti(tN), and Mi(tN) are the axial force, torque, and bending moment on i-th FEA beam element at time tN. Ai, Ix,i, and Iyz,iare cross section area, area moment of inertia, and bending moment of inertia of i-th FEA beam element.

Kinetic energy is the energy that an object possesses due to its motion. The kinetic energy may be decomposed into a translation component and a rotary component. The foregoing kinetic energy components are illustrated with formulas for calculating them, respectively, inFIGS. 3 and 4. For each FEA beam element, kinetic energy of axial or lateral translational motion may be calculated by the expression:
UKTran=½m|{right arrow over (v)}|2(16)
Here, m is the mass of the beam element, and v the translational velocity vector of mass center of element.
Axial rotational kinetic energy may be calculated by the expression:
UKRot=½Jxω2(17)
Here, Jxis the polar mass moment of inertia of the beam element, and co the axial rotation speed.

Kinetic energy used to tilt the axis of one FEA beam element is illustrated with a formula inFIG. 5. The tilt rotation kinetic energy may be calculated by the expression:
UKRotTilt=½Jyzωtilt2(18)
wherein Jyzis the mass moment of inertia about axis located at beam center and perpendicular to beam axis, and ωtiltthe tilt rotation speed.
The total kinetic energy of drill string are the sum of kinetic energy calculated on each FEA element.

Energy loss in the drilling process is defined as the energy consumed by the work done by contact friction and all types of damping mechanisms (like contact restitution and material damping). Considering the principle of conservation of energy, the energy loss Wloss(tN) at time tNcan be expressed as:
Wloss(tN)Winput(tN)+Winput_PDM(tN)−Wdrilling(tN)−UStrain(tN)−UKinetic(tN)  (20)

An example set of calculations using a method according to the present disclosure may be better understood with reference toFIG. 7. A drill string is illustrated schematically at120. The drill string has selected diameter (internal and external), selected weight, selected moment of inertia, selected elastic properties and a drill bit at a bottom end thereof. Components of the BHA and their respective mechanical properties are shown at122. Arrangement of cutting elements and other mechanical properties of the drill bit are shown at124. Drilling operating parameters (weight on bit, drill string rotational speed) used in the calculations are shown at126. Mechanical interaction properties between the formation (wellbore) and the drill string are shown at128. Finally at130, properties of the formation (rock) being drilled are illustrated. The present example simulation was conducted for 109 revolutions of the drill string. It will be appreciated that any other simulation may be performed for more or fewer drill string rotations as the user may find desirable. Because all of the forces acting on each meshed element of the drill string are calculated, a simulation conducted according to the present disclosure can also calculate the drill string mode of motion, e.g., and without limitation, normal rotary drilling with determinable contact points/lengths between the drill string and the wellbore wall, stick slip motion, lateral vibration of the drill string and/or BHA, whirling motion and axial vibration. As will be explained below, the mode of motion may have a substantial effect on the amount of total applied energy that is ultimately consumed by drilling formations, rather than being dissipated by one or more of the above described mechanisms.

Results of the above simulation are shown graphically inFIG. 8.FIG. 8includes graphs of bit RPM, lateral acceleration on the bit and the rate of drilling the formation (rate of penetration—ROP). It may be observed inFIG. 8that at about 16 seconds, the drill string movement mode changes from “stick-slip” (wherein the drill string becomes momentarily stuck in the wellbore and subsequently is freed to rotate) to “backward whirl” (wherein the axis of the drill string precesses in a direction opposite the rotation of the drill string) and correspondingly consumes energy by frictional contact with the wellbore wall. It may be observed that the ROP drops substantially when the movement mode changes to backward whirl.

FIG. 9shows graphs of both strain and kinetic energy for the same set of conditioned used to generate the graphs shown inFIG. 8. During stick-slip, bending strain energy and translation kinetic energy terms are negligible compared to torsional strain energy and axial rotation kinetic energy. As whirling begins, bending strain energy and translation kinetic energy increase dramatically, and oscillation of torsional strain and kinetic energy substantially vanish because the bit RPM becomes stable.

FIG. 10shows a graph that illustrates during initial drilling, almost all the surface energy input is used to drill the formation. After entering whirling mode, more energy is lost due to the increased contact interactions between the drill string and the wellbore.

FIG. 11shows a graph or applied and consumed power for the simulation shown with reference toFIG. 9. As may be observed inFIG. 11, during initial drilling, almost all the surface energy input is used to drill the formation. After entering whirling mode, more energy is lost due to the increased contact interactions between drill string and wellbore. In this case, only about 40% energy input from surface is used for formation drilling in whirl mode.

It will be appreciated that while stick-slip drilling results in much higher transfer of energy applied to the drill string into drilling formation, stick-slip drilling should be carefully monitored for excessive buildup of torque in the drill string and its sudden release. U.S. Pat. No. 7,140,452 issued to Hutchinson discloses how under certain circumstances, torsional stick-slip may result in the released torque causing certain drill string components to rotationally accelerate such that the breaking torque of threaded connections is exceeded. When selecting drilling operating parameters for use in a method according to the present disclosure, maximum rotational acceleration on torsional release of any part of the drill string should be determined, such that the breaking torque is not exceeded.

FIG. 12shows a comparison of results obtained for hard formations (designated UL_3000) as contrasted with softer formations (designated WE_3000). From the graphed results, it may be readily determined that harder formations tend to have higher lateral vibration on the drill bit and lower bit RPM variation for the used set of drilling operating parameters.

FIG. 13shows graphs of bending strain energy (SE) and translational kinetic energy (KE) when drilling hard formations (UL_3000) as contrasted with softer formations (WL_3000). Drilling hard formation (UL_3000) shows much higher bending strain energy and translational kinetic energy.

Since bending SE and translational KE are calculated based on the entire BHA, these parameters can be used as lateral vibration indices for the entire BHA.

FIG. 14shows graphs for the same formations of the power transmitted to the bit for drilling the formations and the lateral acceleration experienced by the drill bit. In terms of the ratio of energy loss to energy input, more energy is dissipated by contact interactions in hard rock drilling (UL_3000). The foregoing is consistent with the trend of lateral acceleration of two cases (more lateral acceleration means more wellbore contact and more energy loss). It is contemplated that the energy loss ratio could be used an indicator of drilling efficiency.

FIG. 15illustrates an example drill string and BHA for a simulation that includes a drilling motor (shown proximate the drill bit in the left hand panel ofFIG. 15. In the present example, energy input and energy loss may be calculated for both the rotary input at the surface (top drive or rotary table) and the drilling motor. Referring toFIG. 16, energy input for both the top drive and the drilling motor, as well as their respective energy losses are shown graphically. Energy input at the motor is about three times that provided at surface top drive.

FIG. 17shows a graph of power and power loss for both the top drive and the drilling motor. Energy loss is about 12% of the total energy input (top drive [or rotary table]+ motor).

In other embodiments, a different procedure may be used to determine parasitic energy loss, i.e., energy consumed other than by drilling formations. The total energy applied to the drill string (and to the drill bit when a drilling motor is used) is described in Eqs. (5) and (6). The amount of work (energy) consumed by drilling formations is described by Eq. (7). Total energy losses from any or all of the parameters described herein will be represented by the difference between the total energy input (Eqs. 5 and/or 6) and the energy used in drilling formations (Eq. 7).

To summarize the present disclosure and possible benefits of a method according to the present disclosure, subsurface formation drilling is a process in which energy is input at the surface and in some example embodiments by a drilling motor in the drill string. The energy is transferred through the drill string and BHA, and is then used to drill formations below the drill bit. Part of the energy input may be converted to drill string elastic strain/kinetic energy, and as well as being dissipated due to contact friction between the drill string and the wall of the wellbore. The amounts of energy used to drill the formations and the amount of energy lost due to any or all of the foregoing factors may be calculated.

Drill string strain energy and kinetic energy reflect how much energy resides in the drill string in the form of elastic deformation and dynamic motion. These parameters may be used as state indicators for the entire drill string deformation and vibration. Energy loss is an effective measure of drilling efficiency. A transient dynamic simulation method may be useful for energy calculation because such methods output a continuous history of kinetic and force responses of entire drill string.

Clear signatures of strain energy and kinetic energy can be found for different vibration modes using a method according to the present disclosure.

In a further embodiment, if the calculations suggest excessive amounts of input energy are being dissipated by any one or more of the foregoing energy dissipating interactions of the drill string and/or accelerations of the drill string, one or more drilling operating parameters may be adjusted in order to reduce the dissipated energy, thereby transferring more of the input energy into drilling the formations.

The drilling system design can affect drilling energy input and transfer during drilling. Selection of different bits, reamers, mud motors, and other bottom hole assembly tools can affect how effective the energy is utilized to destroy the formation. The disclosed energy calculation based on drilling dynamics simulation can be applied to plan drilling system for a specific job, including selection of drill bits, drilling tools and drill stems, placement of drilling tools, design of well bore sizes and trajectory, selection of drilling parameters, etc. Energy calculation can be conducted based on the planned drill string and wellbore trajectory to assess the energy input requirements for the planned drilling operation. This information can be used to guide the selection of proper surface power supply and downhole drive system (such as motor and turbine). Since kinetic energy and strain energy of drill string represent the energy possessed by drill string in the form of vibration and deformation, they can be used as performance indicators of the entire drill string. In the well planning stage, the kinetic energy for different drilling systems can be calculated and relatively compared to help choose the most stable one (with least kinetic energy) for a specific job. The kinetic energy can be applied to compare the drilling stability of different drilling parameters. The kinetic energy of drill system can be compared to a pre-specified threshold to evaluate if the vibration level is acceptable or not. The strain energy indicator can be utilized to evaluate the robustness of drill string. Lower strain energy means smaller deformation and lower stress. The strain energy can be applied to plan drilling system and practice to lower the drill string lost-in-hole failure risk. The effective usage of drilling energy is to drilling formation. The difference between energy input and energy used for formation drilling is energy loss, which can be used as a drilling efficiency indicator. The energy calculation can be conducted in the planning phase to compare energy loss for different drilling systems and different drilling parameters. Among the several given BHA options and drilling parameter range derived from offset well experiences and tool limits, an optimization process can be performed to select BHA and parameters yielding the lowest energy loss.

During execution phase, simulation of different drilling parameters can be conducted during drilling. Energy calculation can be done for each simulated scenarios to help select favorable drilling parameters or adjust downhole tool functions. The depth-by-depth lithology data of offset well is used to map the formation top in the current well before drilling. This helps select the rock type used in drilling dynamics simulation. A bit wear model can be built into dynamic simulation to predict the dull condition of bit based on the cutter loading conditions, travel velocity, and formation abrasiveness. The downhole logging tool can send the real-time downhole dynamics and mechanics measurement data to surface. These information can be used to calculate the strain and kinetic energy of drill string at the measurement location. When the discrepancy between simulated and measured energy parameters is found, a real-time calibration process for drilling dynamics model is activated to adjust modeling parameters to match the downhole measurements. The calibrated dynamics model can be used to calculate the real-time energy distribution in the drill string and to predict the energy input requirement for the upcoming operations. The kinetic energy indicator can be closely monitored through the real-time simulation to identify the adverse downhole vibration modes (such as stick-slip or backward whirling) based on comparison of indicator with specific thresholds. The strain energy can be calculated during drilling to identify the overloading condition of drill string and to raise warning to driller when a specific threshold is exceeded. A poor drilling efficiency condition can be identified by monitoring when the predicted energy loss ratio is higher than a certain threshold.

The calculation could be conducted during the post well analysis stage. The actual drilling system and parameters used in the job can be simulated to understand energy input, energy transfer, and the energy dissipation. The downhole measurement data from logging tools and surface drilling data can be used to calibrate the dynamics model. The calibrated model is utilized to analyze how the energy is distributed in drill string and to identify the sources/factors leading to poor drilling efficiency condition (high energy loss ratio) and severe shock and vibration (high kinetic energy). The energy calculation can be also used to troubleshoot the cause of downhole tool failures such as twist off. The energy calculation procedure can be applied to evaluate the new proposed drilling system and drilling practices to identify the possible improvement areas for future jobs. A flow chart of one example embodiment of a method according to the present disclosure is shown inFIG. 18, in which at130energy is applied to to a drill string at at least one of a surface of the drill string and by a motor disposed in the drill string to operate a drill bit at a bottom of the drill string. At132an amount of the applied energy not consumed in drilling formations caused by at least one of motion, deformation, and interaction of the drill string is calculated. At134an amount of the applied energy used to drill formations below the drill bit is calculated. Finally, at136at least one of a drill string parameter and a drilling operating parameter to optimize the applied energy used to drill the formations is adjusted.

FIG. 19shows an example computing system100in accordance with some embodiments. The computing system100may be an individual computer system101A or an arrangement of distributed computer systems. The individual computer system101A may include one or more analysis modules102that may be configured to perform various tasks according to some embodiments, such as the tasks explained with reference toFIGS. 2 through 18. To perform these various tasks, the analysis module102may operate independently or in coordination with one or more processors104, which may be connected to one or more storage media106. A display device105such as a graphic user interface of any known type may be in signal communication with the processor104to enable user entry of commands and/or data and to display results of execution of a set of instructions according to the present disclosure.

The processor(s)104may also be connected to a network interface108to allow the individual computer system101A to communicate over a data network110with one or more additional individual computer systems and/or computing systems, such as101B,101C, and/or101D (note that computer systems101B,101C and/or101D may or may not share the same architecture as computer system101A, and may be located in different physical locations, for example, computer systems101A and101B may be at a well drilling location, while in communication with one or more computer systems such as101C and/or101D that may be located in one or more data centers on shore, aboard ships, and/or located in varying countries on different continents).

A processor may include, without limitation, a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

The storage media106may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example embodiment of FIG. the storage media106are shown as being disposed within the individual computer system101A, in some embodiments, the storage media106may be distributed within and/or across multiple internal and/or external enclosures of the individual computing system101A and/or additional computing systems, e.g.,101B,101C,101D. Storage media106may include, without limitation, one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that computer instructions to cause any individual computer system or a computing system to perform the tasks described above may be provided on one computer-readable or machine-readable storage medium, or may be provided on multiple computer-readable or machine-readable storage media distributed in a multiple component computing system having one or more nodes. Such computer-readable or machine-readable storage medium or media may be considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions, or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

It should be appreciated that computing system100is only one example of a computing system, and that any other embodiment of a computing system may have more or fewer components than shown, may combine additional components not shown in the example embodiment ofFIG. 19, and/or the computing system100may have a different configuration or arrangement of the components shown inFIG. 19. The various components shown inFIG. 19may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and/or application specific integrated circuits.