Patent Application
20160117424
Earth formations may be used for various purposes such as hydrocarbon production, geothermal production, and carbon dioxide sequestration. Boreholes are drilled into the earth formations to gain access to them. The boreholes are typically drilled by using a drill string having a drill bit at the far end. Torque and weight are applied to the drill string by a drill rig in order to rotate the drill bit and provide a force to cut through formation rock. Forces other than those applied by the drill rig are also imposed on the drill string. These other forces are applied by the formation itself as it makes contact with the drill string and the drill bit. The total sum of a certain combination of forces acting on the drill string however can cause drilling dysfunctions such as stick-slip and whirl. Unfortunately, drilling dysfunctions can lead to equipment damage, drilling downtime and associated costs. Hence, it would be well received in the drilling industry if methods were developed to predict with a known level of certainty when a drilling dysfunction will occur.
Disclosed is a method for estimating a probability of a drilling dysfunction occurring or a probability of a drilling performance indicator value occurring. The method includes: entering drilling-related data having a probability distribution into a mathematical model of a drill string drilling a borehole penetrating the earth; entering drilling parameters into the model for drilling the borehole; and performing a plurality of drilling simulations using the model, each simulation providing a probability of the drilling dysfunction occurring or a probability of a drilling performance indicator value occurring with associated drilling parameters used in the simulation; selecting a set of drilling parameters that optimizes a drilling objective using the probabilities of the drilling dysfunction occurring or the probabilities of a drilling performance indicator value occurring; and transmitting the selected set of drilling parameters to a signal receiving device; wherein entering drilling-related data, entering drilling parameters, performing a plurality of drilling simulations and selecting a set of drilling parameters are performed using a processor.
Also disclosed is a non-transitory computer readable medium having computer-readable instruction for estimating a probability of a drilling dysfunction occurring or a probability of a drilling performance indicator value occurring that when executed by a computer implements a method that includes: entering drilling-related data having a probability distribution into a mathematical model of a drill string drilling a borehole penetrating the earth; entering drilling parameters into the model for drilling the borehole; performing a plurality of drilling simulations using the model, each simulation providing a probability of the drilling dysfunction occurring or a probability of a drilling performance indicator value occurring with associated drilling parameters used in the simulation; and selecting a set of drilling parameters that optimizes a drilling objective using the probabilities of the drilling dysfunction occurring or the probabilities of a drilling performance indicator value occurring; and transmitting the selected set of drilling parameters to a signal receiving device.
The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike:
A detailed description of one or more embodiments of the disclosed apparatus and method presented herein by way of exemplification and not limitation with reference to the figures.
Disclosed is a method, which may be implemented by a computer for estimating a probability or likelihood of a drilling dysfunction occurring. A mathematical model of a drill string used to drill a borehole is used to perform mathematical simulations of the drilling process. The model is populated with drilling-related data having a probability distribution and with known drilling parameters. A plurality of drilling simulations is performed with each simulation providing whether a drilling dysfunction occurred or not, the drilling parameters used for that simulation, and a probability of the drilling dysfunction occurring or not occurring based upon the probability distribution of the drilling related data entered into the model. A probabilistic stability map can then be generated from all of the data from the plurality of drilling simulations. Once the probabilistic stability map is generated, the map can be displayed to a drilling operator to make decisions for manually controlling the drilling parameters to avoid the drilling parameters that may lead to unstable drilling or dysfunctions. Alternatively or in addition to the operator display, the values of the probabilistic stability map may be entered into a controller for automatically controlling the drilling parameters to avoid the drilling parameters that may lead to unstable drilling or dysfunctions. Computational time for performing the simulations may be reduced by performing the simulations using different models having different fidelity levels of representing the drill string. If a lower fidelity model provides similar results as a higher fidelity model, the lower fidelity model can be used going forward with the corresponding benefit of requiring less computational time to provide quicker results.
Refer now to
The probability of the selected drilling dysfunction occurring may be calculated using various methods. In a first exemplary method as illustrated in
In a second exemplary method as illustrated in
Various mathematical techniques may be used to improve the efficiency of running the Monte Carlo simulations. These techniques may include Markow chain Monte Carlo simulations (e.g., Metropolis algorithm) and variance reduction techniques such as antithetic variates, stratified sampling, importance sampling, and control variates. It can be appreciated that other types of mathematical techniques may be used to perform the simulations such as Random Walk or entering probability distribution functions (where the probability distribution function is described analytically, e.g., f(x)) directly into the models.
In order to improve computational efficiency, the method 20 may also include comparing the output obtained using a high fidelity or complexity model to the output obtained using a lower fidelity or complexity model as illustrated in
From the plurality of drilling simulations, a corresponding plurality of data groups will be provided. Each data group may include (i) the drilling parameters used in the corresponding simulation, (ii) if the selected drilling dysfunction occurred, and (iii) the probability of the combination of the drilling related data used in the simulation occurring and thus the probability of the selected drilling dysfunction occurring. The method 20 may include inputting the data groups into a controller for automatically controlling the drilling parameters to prevent the drilling dysfunction while the borehole is being drilled as illustrated in
It can be appreciated that a plurality of models may be used to perform the drilling simulations with each model modelling a different drilling dysfunction. For example a first model may model stick-slip while a second model may model drill bit whirl or lateral vibrations that exceed a threshold. Each probabilistic drilling stability map associated with each drilling dysfunction may be displayed to a user, as illustrated in
The plurality of data groups may be used to plot a graph of the probability of a selected drilling dysfunction occurring for a particular set of drilling parameters (see right side of
Examples of stick-slip stability maps are now presented. A falling characteristic of the torque with respect to the RPM is assumed which can lead to a self-excitation of the first torsional mode of the system. Two stability borders can be calculated: The first is the transition between no stick-slip and stick-slip if the RPM fluctuation is zero. The second is the transition between stick-slip and no stick-slip if a full stick slip cycle is occurring. These two borders are caused by the nonlinear characteristics of the torque vs. RPM. If the parameters of the falling torque characteristics and the modal damping are constant these borders are lines. A transition occurs directly at these lines. In real applications, the transition is a zone with different probabilities of stick slip because of the variation of the damping and parameters of the falling torque characteristics.
In addition to predicting drilling stability with a known probability for certain drilling dysfunctions, the probabilistic techniques disclosed herein may be used to select drilling parameters that optimize one or more drilling performance indicators such as ROP as illustrated in
It can be appreciated that the Optimizer may be used to optimize drilling parameters such as ROP and build rate including expected value E[ ], variance Var[ ], convariance COV, correlation Con and other stochastical moments E[X̂k] related to drilling performance. The optimization may be weighted with k_1, k_2, . . . (can also be negative values). An abitrary function f can be used which combines theses values. A function such as Max(k1E(ROP)+k2E(Build Rate)+k3Var(ROP)+k4Var(Build Rate)+f(COV, E, Var, Corr, E(Xk))) may then be maximized. Constraints may be used for the probability of dysfunctions or other values as illustrated in
It can be appreciated that the probabilistic drilling stability maps and the probabilistic drilling performance maps may be used to design the BHA 10. By selecting certain BHA design parameters such as dimensions, weights, and material characteristics, these design parameters can be entered into the drill string model. Drilling simulations may then be performed using the model to calculate the associated probabilistic drilling stability maps and the probabilistic drilling performance maps. These maps may then be analyzed to determine if the design parameters lead to acceptable drilling performance or not. If not, then the design parameters may be changed and new maps calculated using the disclosed techniques. This may result in an iterative process until design parameters are selected that lead to acceptable drilling performance.
It can be appreciated that the model used for performing the drilling simulations may also be configured to predict a borehole drilling characteristic such as borehole path, dogleg severity, build rate, and walk rate. The drilling simulations may then be used to determine a probability of a certain borehole characteristic value occurring based on the entered drilling parameters and the probability distributions of the entered drilling-related data. Unknown proposed parameters of the optimization and/or prediction probabilistic techniques (e.g., friction factor, formation properties, and drill bit aggressiveness) are considered by estimating their mean values and their distribution based on offset wells, historical data or laboratory experiments.
In support of the teachings herein, various analysis components may be used, including a digital and/or an analog system. For example, the downhole electronics 9, the computer processing system 11, or the drilling parameter controller 13 may include digital and/or analog systems. The system may have components such as a processor, storage media, memory, input, output, communications link (wired, wireless, pulsed mud, optical or other), user interfaces, software programs, signal processors (digital or analog) and other such components (such as resistors, capacitors, inductors and others) to provide for operation and analyses of the apparatus and methods disclosed herein in any of several manners well-appreciated in the art. It is considered that these teachings may be, but need not be, implemented in conjunction with a set of computer executable instructions stored on a non-transitory computer readable medium, including memory (ROMs, RAMs), optical (CD-ROMs), or magnetic (disks, hard drives), or any other type that when executed causes a computer to implement the method of the present invention. These instructions may provide for equipment operation, control, data collection and analysis and other functions deemed relevant by a system designer, owner, user or other such personnel, in addition to the functions described in this disclosure. Processed data such as a result of an implemented method may be transmitted as a signal via a processor output interface to a signal receiving device. The signal receiving device may be a display monitor or printer for presenting the result to a user. Alternatively or in addition, the signal receiving device may be memory or a storage medium. It can be appreciated that storing the result in memory or the storage medium will transform the memory or storage medium into a new state (containing the result) from a prior state (not containing the result). Further, an alert signal may be transmitted from the processor to a user interface if the result exceeds a threshold value.
Further, various other components may be included and called upon for providing for aspects of the teachings herein. For example, a power supply (e.g., at least one of a generator, a remote supply and a battery), cooling component, heating component, magnet, electromagnet, sensor, electrode, transmitter, receiver, transceiver, antenna, controller, optical unit, electrical unit or electromechanical unit may be included in support of the various aspects discussed herein or in support of other functions beyond this disclosure.
Elements of the embodiments have been introduced with either the articles “a” or “an.” The articles are intended to mean that there are one or more of the elements. The terms “including” and “having” are intended to be inclusive such that there may be additional elements other than the elements listed. The conjunction “or” when used to connect at least two terms is intended to mean any term or combination of terms. The term “configured” relates one or more structural limitations of a device that are required for the device to perform the function or operation for which the device is configured. The terms “first” and “second” do not denote a particular order, but are used to distinguish different elements. The term “optimize” does not necessarily relate to selecting a maximum or minimum value but may include selecting a value within a selected range of a maximum or minimum value or selecting a value within a selected range of a desired value based upon the circumstances for optimization.
The flow diagram depicted herein is just an example. There may be many variations to this diagram or the steps (or operations) described therein without departing from the spirit of the invention. For instance, the steps may be performed in a differing order, or steps may be added, deleted or modified. All of these variations are considered a part of the claimed invention.
While one or more embodiments have been shown and described, modifications and substitutions may be made thereto without departing from the spirit and scope of the invention. Accordingly, it is to be understood that the present invention has been described by way of illustrations and not limitation.
It will be recognized that the various components or technologies may provide certain necessary or beneficial functionality or features. Accordingly, these functions and features as may be needed in support of the appended claims and variations thereof, are recognized as being inherently included as a part of the teachings herein and a part of the invention disclosed.
While the invention has been described with reference to exemplary embodiments, it will be understood that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications will be appreciated to adapt a particular instrument, situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.
