This patent application is a divisional of prior U.S. patent application Ser. No. 11/564,474 filed Nov. 29, 2006 now U.S. Pat. No. 7,645,124, which is claiming priority to U.S. Provisional Patent Application No. 60/740,377, filed Nov. 29, 2005, both of which are incorporated herein in their entirety by this reference.
This invention relates generally to estimation and control of resonant behavior in a system, and more particularly to estimation and control of resonant behavior in systems having two inertias coupled by a compliant connection, with such systems including those prone to exhibiting stick-slip behavior, such as systems and plants related to drilling for, and pumping oil.
In general, any drive connection in a mechanical system exhibits some degree of compliance, i.e. a tendency to yield or bend under load, within the elastic limit of the material, or materials, of the components making up the connection. As a result of this compliance, a driving force exerted at one end of the connection causes the connection to stretch, bend, and/or twist, depending upon the nature of the connection, in such a manner that the driving force will be slightly out of phase with a corresponding reaction of a driven element at the opposite end of the connection, due to inertia of the driven component which must be overcome in order for the driving force to cause a motion of the driven element consistent with the motion of a driving element applying the driving force.
Under certain circumstances, depending upon construction of the system, compliance in the connection will cause an undesirable oscillating or resonant motion to be set up between the driving and driven elements.
Such oscillating behavior is sometimes observed in a system having an engine connected to an engine testing dynamo through a connection including an in-line torque sensor. Such torque sensors typically include a resilient element operatively joining an input element and an output element of the torque sensor. The resilient element allows the input and output elements to twist slightly, with respect to one another, in response to torque being transmitted through the torque sensor. This twisting can be measured and used to determine the torque being transmitted by the coupling.
During an increase and/or decrease in torque, however, the resilient element may cause the system to oscillate as energy is alternately stored and released in the resilient element, until equilibrium is achieved. Such oscillation can be damaging or otherwise detrimental to operation of the system and its components. It is desirable, therefore, to provide an apparatus and method for estimating such behavior, and for controlling the system in such a manner that the undesirable oscillatory or resonant behavior is precluded and/or held within acceptable bounds. It is also highly desirable, in some circumstances, to provide for such control without having sensors located at the driven element, i.e. at the dynamo in the example given above, in order to remove complexity and cost and to improve reliability of the system.
In some systems, oscillating or resonant behavior takes a form known as stick-slip behavior. Stick-slip behavior refers to an undesired intermittent form of motion that sometimes occurs between relatively moving parts where the coefficient of kinetic friction between the parts is less than the coefficient of static friction between the parts. Contacting surfaces of the parts will stick to one another until a driving force, being exerted on one of the parts by a drive element to cause relative movement between the parts, reaches a value high enough to overcome the static frictional force between the contact surfaces.
Due to the fact that the static coefficient of friction is higher than the kinetic coefficient of friction, once the static friction force is overcome by the driving force, the contact surfaces of the parts will tend to move freely and rapidly with respect to one another.
Because there is an inherent springiness (compliance) in the drive element applying force between the parts, the drive element will tend to stretch or compress, or wind up, as force is applied to the movable part while the contact surfaces are being held in contact by the static friction force. Once relative motion occurs, this compression, tension, or winding-up of the drive element will cause rapid movement between the parts, to release the energy stored in compression, tension or wind-up of the drive element. Once the stored energy is released, however, through rapid relative movement between the parts, the relative velocity between the contact surfaces will drop to the point that the static friction force will once again cause the parts to stick to one another, and thereby preclude further relative motion, until sufficient compression, tension, or wind-up of the drive element once again occurs, to overcome the static frictional force and cause slipping of the contact surfaces relative to one another.
Such stick-slip behavior is known to sometimes occur in metal working equipment, for example, where a drill bit or milling cutter must be driven by a power source located some distance from the point at which material removal is occurring, such that the drill bit or cutter must have a long shank, and/or be connected to a long drive shaft.
Stick-slip behavior is also sometimes encountered in machinery used in drilling for, or pumping fluids, such as gas, water, or oil, out of the ground. In such applications, long shafts, having lengths of hundreds or thousands of feet, may connect a drilling or pumping apparatus located far below ground level to a shaft drive mechanism located above ground level. Such long shafts have considerable inherent springiness, both axially and radially. This considerable springiness allows a significant amount of energy to be stored in the shaft, if the underground components stick to one another, such that when the torsional force due to wind-up of the shaft becomes high enough to cause the underground parts to break free from one another, they will slip relative to one another at a very high rotational speed, until the energy stored in the shaft is dissipated.
In addition to placing significant undesirable strain on the working components of the system, stick-slip operation of a pump also will substantially reduce the pumping capacity of the pump. While the parts are stuck to one another no relative motion or pumping is occurring, and during a portion of the stick-slip cycle in which the parts are moving very rapidly with respect to one another, pumping may also not be occurring.
Stick-slip operation, and its detrimental effects, is further discussed in a United States Patent Application No. US 2004/0062658 A1, published Apr. 1, 2004, to Beck, et al., assigned to the assignee of the present invention, the disclosure and teachings of which are incorporated herein in their entirety.
Prior approaches to dealing with a system exhibiting stick-slip behavior, have sometimes utilized sensors located adjacent to the contacting surfaces subject to stick-slip behavior. In oil pumping operations, for example, this has sometimes required placement of sensing equipment a mile or more below the earth's surface and making connections to a controller located above ground. Such sensors tend to be quite expensive to produce and maintain, and are prone to failure due to the hostile environment in which they are located. Should repair of the sensing elements be required, significant interruption to the pumping process is incurred, in pulling the sensing unit back up to the surface of the ground where it can be repaired and/or replaced.
It is highly desirable, therefore, to provide an improved method and/or apparatus for estimating and controlling undesirable oscillatory or resonant behavior in a system prone to such behavior, and particularly in systems which may be prone to stick-slip behavior. It is also desirable to provide an apparatus and/or method for controlling such systems with a minimal number of transducers, and preferably without the necessity for having such transducers located near a driven element of the system.
An improved method and apparatus for estimating precluding stick-slip, or other oscillatory behavior is provided. In some embodiments, estimating and precluding stick-slip, or other oscillatory behavior is accomplished with a “virtual transducer,” without the need for having sensors located adjacent to a driven element, or adjacent to contact surfaces at which stick-slip relative motion may occur. As a result, significant advantage is provided in an oil pumping system, for example, by eliminating the undesirable cost and difficulty of locating sensors in a hostile environment far below the surface of the ground.
In one embodiment, stick-slip behavior, or other oscillatory behavior, of a system may be estimated and related to parameters measurable in a drive apparatus of the system. In an application such as, for example, an oil pumping system having a progressive cavity pump driven by an electric motor, parameters such as velocity, torque, rotational angle, and input power, all of which are measurable above ground at the drive apparatus, may be utilized in detecting and estimating stick-slip behavior.
In another embodiment, parameters measurable at a drive mechanism, such as the speed, torque, rotational angle, and power of an electric motor driving a driven element in a system susceptible to stick-slip behavior, may be utilized, in a “virtual transducer,” for controlling the system in a manner which precludes stick-slip, or other oscillatory or resonant, behavior of the driven element. In some embodiments, prone to stick-slip behavior, relative motion between contacting surfaces in the driven element is controlled in such a manner that, after sufficient force is applied to overcome the static friction force between the contacting surfaces and break them free from one another, relative motion between the surfaces is controlled at a high enough relative speed that the surfaces are precluded from contacting one another, so that stick-slip behavior is precluded.
One embodiment provides a “virtual transducer,” for use in controlling a system prone to stick-slip, or other oscillatory or resonant, behavior, thereby precluding the need for providing one or more of the sensors which had to be located adjacent the driven element in prior approaches to controlling such systems.
Other aspects, objects and advantages will become apparent from the following brief description of drawings and attachments, and the detailed descriptions provided within the attachments.
While the invention will be described in connection with certain preferred embodiments, there is no intent to limit it to those embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents as included within the spirit and scope of the invention as defined by the appended claims.
A progressing cavity pump (PCP) 112 is mounted at the lower end of the tube 106 and includes a helix type of pump member 114 mounted inside a pump housing. The pump member is attached to and driven by a pump rod string 116 which extends upwardly through the tube and is rotated by a drive motor 118 in a conventional well head assembly 120 above ground level. The tube 106 has a liquid outlet 122 and the casing 104 has a gas outlet 124 at the upper end above ground level 126. These elements are shown schematically in
The operation of the pump 112 is controlled by a pump control system and method including a stick-slip estimator and controller in accordance with the present invention. For purposes of illustration, the pump control system 130 is described with reference to an application in a pump system that includes a conventional progressing cavity pump. The progressing cavity pump includes an electric drive system 132 and motor 118 that rotates the rod string 116 that includes helix portion 114 of the pump 112. The rod string 116 is suspended from the well head assembly 120 for rotating the helix 114 that is disposed near the bottom 134 of the well.
The rod string 116 is driven by an electric motor 118, the shaft of which can be coupled to the rod string through a gearbox 136 or similar speed reduction mechanism. The motor 118 can be a three-phase AC induction motor designed to be operated from line voltages in the range of 230 VAC to 690 VAC and developing 5 to 250 horsepower, depending upon the capacity and depth of the pump. The gearbox 136 converts motor torque and speed input to a suitable torque and speed output for driving the rod string 116 and helix 114 carried thereby.
Turning now to
Although not required, the stick slip estimator/controller will be described in the general context of computer-executable instructions, such as program modules, being executed by the processing unit 150. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the invention may be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.
The self-sensing control arrangement described above provides nearly instantaneous estimates of motor velocity, crank angle, and torque, which can be used for both monitoring and real-time, closed-loop control of the pump, including the stick-slip behavior. Voltages and currents are sensed to determine the instantaneous electric power drawn from the power source by the electric motor operating the pump and the crank angle of the motor 118. As the rod 116 (
Turning now to
Motor vector controller 204 generates motor current commands Imc and voltage commands Vmc based upon signals from control modules 206. Control modules 206 receives estimates of system parameters from system model 202 and may have, for example, a fluid level feedforward control module that outputs a motor torque feedforward signal and a fluid level feedback control module that outputs a motor speed command. The motor speed command and the motor torque feedforward signal can then be combined to generate motor current commands Imc and voltage commands Vmc. Interface devices in block 208, which can be digital to analog converters, convert the current commands Imc and voltage commands Vmc into signals which can be understood by the drive 132. These signals are shown as Ic for motor current commands and Vc for motor winding voltage commands.
Turning now to
where T is the sampling period. The estimated speed is derived from the calculation
where T is the sampling period. Additionally, the crank acceleration (Alphac) is derived by differentiating the crank speed Wc:
Note that the Te(z) and Wc(z) inputs were passed through low pass filters prior to the above calculations. For best performance, the low pass filters on the Wc and Te inputs should have the same frequency response and delay as each other.
In the embodiment shown in
where P is a derivative operator
In another embodiment, Te is estimated while Ac and Wc are measured with an encoder. Turning now to
Simulations were performed to analyze and determine which types of regulator schemes would work with respect to stick-slip. All regulation schemes were tuned for a natural frequency equivalent to the plant resonant frequency for consistency.
Table 1 below documents the simulated regulator results. Vmax refers to the maximum crank rpm encountered. Tmax refers to the maximum electrical torque. Pmax refers to the maximum instantaneous horsepower. These maximum values should be minimized to reduce drive sizing requirements.
The simulation results show that the linear quadratic regulator exhibits the best stick-slip control response (i.e., minimized surface velocity, torque, and power). One of the drawbacks with the linear quadratic regulator is that tuning of the regulator is a manual weighting process which, while intuitive, is required to be done for each system. The next best alternative to the linear quadratic is the ITAE full state feedback regulator which has an analytic solution for the regulator gains.
From the foregoing, it can be seen that a finite difference state estimator has been described that provides accurate real-time estimates of unmeasurable states. In the embodiments described, the unmeasurable states are down-hole pump states (e.g., pump speed and angle). While a single-section state estimator has been described, a multi-section finite difference state estimator can also be used where each node of the multi-section finite difference state estimator estimates the angle and speed of each section in the multi-section state estimator. An example of this would be in a pumping situation where there are multiple rod sections and the estimated speed and angle of each rod section is needed with higher precision than a single-section state estimator provides. An example of this would be the multi-spring finite difference state estimator shown in
Making Kfd a 4ÎNr matrix allows that gains to be varied along the rod length, which provides the capability to handle varying diameter rods.
While the invention is described herein in connection with certain preferred embodiments, there is no intent to limit it to those embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents within the spirit and scope of the invention.
The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) is to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.
Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.