Fast sucker rod pump downhole indicator diagram estimation for inclined well

Abstract

Systems and methods provided herein relate to pump systems. The pump system includes a pump disposed within a well, an actuator operable to move a rod including a ground end coupled to the actuator and a downhole end coupled to the pump, and a controller. The controller is configured to identify a first impulse response and a second impulse response associated with the pump system based on a first model of the pump system. The controller is further configured to generate a second model of the pump system based on the first impulse response and the second impulse response. The controller is further configured to operate the pump system based on a second model.

Description

[0001] Cross-reference to related applications

[0002] This application claims the benefit of and priority to U.S. Provisional Patent Application No. 63 / 431,156, filed on December 8, 2022, the entire contents of which are incorporated herein by reference. Background Art

[0003] Various types of equipment can be used in underground environments. As an example, a pump system can be used to move fluid in a well in an underground environment. U.S. Patent No. 8,036,829 describes the analysis and control of a reciprocating pump system. Summary of the Invention

[0004] One implementation of the present disclosure relates to a pump system. The pump system includes a pump disposed within a well, an actuator operable to move a rod, and a controller. The rod includes a surface end coupled to the actuator and a downhole end coupled to the pump. The controller is configured to identify a first impulse response and a second impulse response associated with the pump system. The identification includes measuring a first set of position data associated with the surface end of the rod; and, based on a first model of the pump system and the position data, generating a first set of data associated with a simulated operation of the pump system with a load stimulus and a second set of data associated with a simulated operation of the pump system without the load stimulus. The first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data. The controller is further configured to generate a second model of the pump system. Generating the second model of the pump system includes measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values of a downhole condition of the rod based on the identified first impulse response, force data, and position data; and estimating one or more position values of the downhole condition of the rod based on the identified second impulse response and the one or more force values. The controller is further configured to operate the pump system based on the second model.

[0005] Another embodiment of the present disclosure relates to a method for controlling a pump system. The pump system includes a pump disposed within a well and an actuator operable to move a rod, the rod including a surface end coupled to the actuator and a downhole end coupled to the pump. The method includes identifying a first impulse response and a second impulse response associated with the pump system. The identification includes measuring a first set of position data associated with the surface end of the rod; and generating, based on a first model of the pump system and the position data, a first set of data associated with simulated operation of the pump system with a load stimulus and a second set of data associated with simulated operation of the pump system without the load stimulus. The first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data. The method also includes generating a second model of the pump system. Generating the second model of the pump system includes measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values for a downhole condition of the rod based on the identified first impulse response, the force data, and the position data; and estimating one or more position values for the downhole condition of the rod based on the identified second impulse response and the one or more force values. The method also includes operating the pump system based on the second model.

[0006] Another embodiment of the present disclosure relates to a controller for controlling a pump system. The pump system includes a pump disposed in a well and an actuator operable to move a rod, the rod including a surface end coupled to the actuator and a downhole end coupled to the pump. The controller includes one or more processors and a memory. The one or more processors are configured to identify a first impulse response and a second impulse response associated with the pump system. The identification includes: measuring a first set of position data associated with the surface end of the rod; and generating a first set of data associated with a simulated operation of the pump system with a load stimulus and a second set of data associated with a simulated operation of the pump system without the load stimulus based on a first model of the pump system and the position data. The first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data. The one or more processors are also configured to generate a second model of the pump system. Generating a second model of the pump system includes: measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values for a downhole condition of the rod based on the identified first impulse response, the force data, and the position data; and estimating one or more position values for the downhole condition of the rod based on the identified second impulse response and the one or more force values. The one or more processors are further configured to operate the pump system based on the second model.

[0007] Some embodiments relate to a controller for controlling a pump system including a pump configured for use at a well. The controller includes one or more processors and a memory. The one or more processors are configured to provide a first impulse response using a first model in response to a surface position input associated with the pump and a surface load input associated with the pump. The first model is a neural network. The one or more processors are further configured to provide a downhole position associated with the pump and a downhole load associated with the pump using a second model in response to the surface position input associated with the pump, the surface load input associated with the pump, and the first impulse response. The second model is a regression model or a neural network model. The one or more processors are further configured to operate the pump system using the second model.

[0008] Some embodiments relate to a controller for controlling a pump system including a pump configured for use at a well. The controller includes one or more processors and a memory. The one or more processors are configured to provide a downhole position associated with the pump and a downhole load associated with the pump using a model, the model being a regression model or a neural network model trained using well-specific data, in response to a surface position input associated with the pump and a surface load input associated with the pump. The one or more processors are further configured to operate the pump system using a second model.

[0009] This summary is illustrative only and is not intended to be limiting in any way.Other aspects, inventive features, and advantages of the devices or processes described herein will become apparent from the detailed description set forth herein in conjunction with the accompanying drawings, in which like reference numerals refer to like elements. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Various objects, aspects, features and advantages of the present disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference numerals identify corresponding elements throughout. In the drawings, like reference numerals generally indicate identical, functionally similar and / or structurally similar elements.

[0011] Figure 1 is a schematic diagram of a system including a pump disposed in a subterranean environment, according to one embodiment.

[0012] Figure 2 is an operation according to one embodiment Figure 1 Schematic diagram of the pump assembly method.

[0013] Figure 3 is a schematic diagram of an instrumented pump system and a dynamometer diagram illustrating operation of the pump system based on measurements of the instrumented pump system according to one embodiment.

[0014] Figure 4According to one embodiment, a method for generating Figure 3 A flow chart illustrating the method of the dynamometer diagram.

[0015] Figure 5 is a flow chart of a method for generating a diagnosis according to one embodiment.

[0016] Figure 6 According to one embodiment, a method for training Figure 5 Flowchart of the method for the recurrent neural network model used in the method shown.

[0017] Figure 7 According to one embodiment Figure 5 Block diagram of the recurrent neural model used in the method shown.

[0018] Figure 8 According to one embodiment, a method for training Figure 5 A block diagram of the method showing the regression model used in the method. DETAILED DESCRIPTION

[0019] Before turning to the drawings that illustrate certain exemplary embodiments in detail, it should be understood that the present disclosure is not limited to the details or methods set forth in the specification or shown in the drawings. It should also be understood that the terminology used herein is for descriptive purposes only and should not be considered as limiting.

[0020] The present disclosure relates to pump systems, including but not limited to estimating one or more conditions associated with a downhole pump system and operating the pump system according to these conditions. A reciprocating pump system, such as a sucker rod pump (SRP) system, can extract fluid from a well and employs a downhole pump connected to a drive source (e.g., an actuator) at the surface. A rod string connects the ground drive force to the downhole pump in the well. During operation, the drive source cyclically raises and lowers the downhole pump, and with each stroke, the downhole pump lifts the well-produced fluid toward the surface. For example, during the upward movement of each stroke, a fixed valve at the bottom opens, and fluid is sucked into the bottom side below the piston, while the fluid at the top of the piston is lifted. During the downward movement of each stroke, a traveling valve opens and a fixed valve closes, which allows the cylinder at the top of the piston to be refilled with fluid. If the pump is partially filled with gas, there will be a delay before the traveling valve opens. In some embodiments, the pumping system is used in the oil industry, the water industry, the waste industry, and general processing / manufacturing plants. In some embodiments, the systems and methods provide condition monitoring of equipment involved in the oil, water, waste, and general processing / manufacturing industries. In some embodiments, the systems and methods are used for integrated wellsite automation products in the field, integrated cloud products (e.g., reservoir monitoring, modeling, verification, planning, optimization), and statistical data analysis for process and design improvements. In some embodiments, the systems and methods provide process estimation for SRP automation in deviated wells.

[0021] Now refer to Figure 1 , illustrates a pump system 100 according to some embodiments. System 100 includes a pump assembly 101 driven by a pump drive system 104, which is operably coupled to a controller 122. For example, pump assembly 101 and drive system 104 can be arranged as a beam pump. In some embodiments, system 100 also includes a walking beam 138 that reciprocates a rod string 144. Rod string 144 can include a polished rod portion 146 that can move within a bore of a stuffing box 150 of a wellhead assembly, which includes a discharge port in fluid communication with a flow line 152. Rod string 144 can be suspended from walking beam 138 via one or more cables 142 suspended from a horsehead 140 for actuating a downhole pump 110 of pump assembly 101, where downhole pump 110 is positioned in a well 102. For example, well 102 can be in a subterranean environment, and downhole pump 110 can be positioned near a bottom 112 of well 102.

[0022] In some embodiments, the well 102 may be a cased well or an open well. For example, a partially cased well may include one or more open well sections. Figure 1As shown, the well 102 includes a casing 106 defining a cased bore, wherein a tubing 108 is disposed within the cased bore. An annular space may exist between the outer surface of the tubing 108 and the inner surface of the casing 106.

[0023] In some embodiments, the walking beam 138 is actuated by a link arm (or multiple link arms) that reciprocate via a crank arm (or multiple crank arms) 134 driven by a prime mover 130 (e.g., an electric motor, etc.). For example, the prime mover 130 can be coupled to the crank arm 134 via a gear reduction mechanism, such as the gears of a gearbox 132. In some cases, the prime mover 130 is a three-phase AC induction motor that can be controlled via the circuitry of the controller 122, which can be connected to a power source. The gearbox 132 of the pump drive system 104 can convert the motor torque into a low-speed, high-torque output that drives the crank arm 134. The crank arm 134 can be operably coupled to one or more counterweights 142 that are used to balance a rod 144 and other equipment suspended from the horse head 140 of the walking beam 138. Balance can be provided by pneumatic cylinders, such as those found on air balance units.

[0024] In some embodiments, the downhole pump 110 is a reciprocating type pump that includes a plunger 116 attached to the end of a rod string 144 and a pump barrel 114 that can be attached to the end of a tubing 108 in the well 102. The plunger 116 can include a traveling valve 118 and a stationary valve 120 positioned at or near the bottom of the pump barrel 114. During operation, for an upstroke in which the rod string 144 translates upward, the traveling valve 118 can close and lift fluid (e.g., oil, water, etc.) above the plunger 116 to the top of the well 102, and the stationary valve 120 can open to allow additional fluid from the reservoir to flow into the pump barrel 114. On a downstroke in which the rod string 144 translates downward, the traveling valve 118 can open and the stationary valve 120 can close in preparation for a subsequent cycle. Operation of the downhole pump 110 may be controlled so as to maintain a fluid level in the pump barrel 114 that is sufficient to maintain the lower end of the rod string 144 in fluid throughout its stroke.

[0025] As an example, system 100 may include a beam pump system. As illustrated, a prime mover may rotate a crank arm, the movement of which is converted to reciprocating motion by a beam. The beam may include a counterweight or compression cylinder to help reduce the load on the beam pump system during the upstroke. The beam may be attached to a polished rod by a cable suspended from a horse head located at the end of the beam. The polished rod may pass through a stuffing box and be operatively coupled to a rod string. As illustrated, the rod string may be raised and lowered within a production tubing in a cased well by the reciprocating motion of the beam, thereby enabling a downhole pump to capture and lift formation fluid in the tubing in a direction toward the surface (e.g., utilizing a flow vector component relative to gravity) by directing the fluid to a pumping tee in the flow line.

[0026] As an example, the prime mover can be an internal combustion engine or an electric motor that provides power to the pumping unit. As an example, the prime mover can transmit high-speed, low-torque power to a gear reducer that converts this energy into low-speed, high-torque energy that is utilized by the surface pump. Figure 1 As shown, a beam pumping unit, beam pump system, or simply beam pump, converts the rotary motion of a prime mover into a reciprocating vertical motion that raises and lowers a rod connected to a subsurface pump.

[0027] Some aspects of the system may include prime mover type; pumping unit size, stroke length and speed setting; rod diameter and tubing diameter; and downhole pump diameter, for example based at least in part on reservoir fluid composition, wellbore fluid depth and reservoir productivity.

[0028] As an example, a design framework can facilitate design decisions such as achieving a desired pump rate to achieve a production target without overloading the system or overwhelm- ing the formation's ability to deliver fluid to the wellbore.

[0029] Beam pumps can be constructed in a variety of sizes and configurations. Some systems include design aspects that can be aimed at better managing torque, rod wear, and / or footprint. For example, some design aspects consider placing counterweights on the crank arm or on the beam, and using compressed air instead of weights to help balance the load. Other examples may involve changing the position of the crank, gear reducer, and motor relative to the beam, as well as alternative beam designs, where such factors may change the system load.

[0030] As an example, the system can place heavier rods, or sinker rods, in the lower section of the rod string to hold the rod string under tension, which reduces buckling and can help prevent contact with the pipe wall. The rod string can also include stabilizer rods between the sinker rods to center the rods, further reducing pipe wear.

[0031] Rod guides, which can be made of reinforced plastic, can be molded into the steel rod at a depth where engineers predict the rod will experience lateral loads due to a deviated wellbore path. The guides can act like bearings between the tubing wall and the rod to prevent wear on the rod and tubing. Sliding guides can move between the molded guides during pump cycles, aiding production by scraping wax from the tubing wall, which helps prevent well plugging. Rod rotators or tubing rotators can be used to rotate the rod a fraction of a full revolution with each stroke of the pumping unit to further extend rod string life. As an example, the slow rotation of the rod guides can help scrape wax from the tubing wall.

[0032] The sucker rod can be connected to the surface pumping unit via a polished rod. For example, the polished rod, made of standard alloy steel and hard-surfaced sprayed metal coating, can support the loads generated during the pump cycle and help ensure a seal with a stuffing box located at the top of the well. The stuffing box can be attached to the wellhead or pumping tee and can form a low-pressure tight seal against the polished rod. This seal can form a barrier between the well and the atmosphere and can allow flow to be delivered to the flow line, for example, via the pumping tee.

[0033] Figure 2 A cross-sectional view of downhole pump 110 is shown illustrating a portion of rod 144 , pump barrel 114 , plunger 116 , traveling valve 118 , and stationary valve 120 positioned at or near the bottom of pump barrel 114 . Figure 2 Further shown are openings 117 for fluid inflow, and chamber 119, which is shown located in a space at least partially disposed between traveling valve 118 and fixed valve 120. Downhole pump 110 is an example of a pump mechanism that can move a fluid, where the fluid can vary with respect to time. For example, the fluid can be a liquid and / or a gas. For example, the fluid can include entrained solids, semi-solids, etc.

[0034] Figure 2An example of method 200 is shown with actions or states 210, 220, 230, and 240, which can be part of a cycle (e.g., a cycle action, a cycle state, etc.). For action 210, pump 110 has reached the maximum downward reach of the cycle. In action 220, the beam can begin its upward movement, causing rod 144 and plunger 116 to be pulled upward, thereby forcing the ball of traveling valve 118 to be seated on traveling valve 118. This upward movement reduces the pressure in pump chamber 119 until it is less than the pressure at pump inlet 117. The ball in stationary valve 120 can then disengage from its seat, allowing formation fluid to enter via inlet 117 and flow to pump chamber 119. For action 230, when plunger 116 is at the end of its upward stroke, stationary valve 120 is closed. As the plunger travels downward, the pressure experienced by pump chamber 119 increases, pushing the ball in traveling valve 118 off the seat of traveling valve 118. As plunger 116 continues to move downward in pump 110, action 240 allows formation fluid to flow from pump chamber 119 via plunger 116 into the tubing. One cycle can include actions 210, 220, 230, and 240. Such a cycle can be repeated thousands of times per day. The fluid displaced into the tubing can be transported toward the surface on subsequent upward strokes of plunger 116.

[0035] Figure 3 An example of a system 300 is shown having a controller 322 and various sensors including position sensors and load sensors. For example, for position sensors, consider an inclinometer 332 and a proximity switch 333 (e.g., a Hall effect sensor); and, for load sensors, consider a load cell 334, a current sensor 335, and a beam transducer 336. These sensors can be operatively coupled to the controller 322 (e.g., via wires and / or wirelessly coupled to the controller 322 through a wireless circuit system). As an example, the load cell 334 can be a load-capable dynamometer attached to a polished rod for acquiring dynamic data that can be transmitted to and / or otherwise accessed by one or more pieces of equipment.

[0036] The controller may utilize sensor data to calculate rod load (eg, surface conditions) and incorporate various models (eg, algorithms) to estimate downhole pump fill (eg, downhole conditions).

[0037] A common challenge in downhole pump operation is the ingress of gas into the pump, resulting in fluid slam or gas jam. Fluid slam occurs when the plunger rapidly travels downward through low-pressure gas and then suddenly impacts the liquid flow; the resulting compression shock can damage the rod string and the prime mover's gearbox. Gas jam is less destructive and occurs when the plunger travels downward through high-pressure gas. Both conditions reduce system efficiency.

[0038] To combat gas interference, a gas separator may be placed below the pump to redirect the gas into the wellbore annulus surrounding the pump.Other modifications may be made to the completion to offset or reduce the effects of heavy oil and sand or other produced solids.

[0039] Operators can diagnose gas interference, liquid flow slugging severity, and various other operating conditions using a dynamometer that plots rod tension against downhole displacement measurements at the surface and at the pump. The ideal downhole diagram, called a dynamometer card, is rectangular and represents a full pump. Deviations from the ideal shape can indicate performance issues such as gas interference, system leaks, a stuck pump, a detached rod, and various other anomalies that can be identified and resolved automatically or through manual intervention.

[0040] Rod pumping systems are a very common form of artificial lift because they are relatively inexpensive to install and operate and have a relatively long lifespan. Rod pumping systems are "simple" machines with a long and well-documented history in the industry, and they are often able to adjust to meet changing well or field conditions.

[0041] The use of rod pumps is likely to increase as the industry continues to expand its involvement in shale formations and other unconventional plays, which require operators to develop each field using a large number of relatively low-flow wells. The initial high pressures and high production rates from these hydraulically fractured horizontal wells are followed by lower bottomhole pressures and steep production decline rates; production is possible through the use of artificial lift systems, where rod pumps tend to be effective at these low rates.

[0042] Now refer to Figure 3, shows a graphical representation of a dynamometer diagram for a pump system (e.g., pump system 100) according to some embodiments. A dynamometer diagram is a record produced by a dynamometer. A dynamometer is an instrument used for sucker rod pumping that records the change between polished rod load and polished rod displacement. The dynamometer diagram can be used in the oilfield industry (and other settings) as a force versus position relationship to assess the integrity of downhole displacement pumping conditions. Downhole forces are estimated from direct surface force and position measurements at the polished rod or related measurements using a mathematical model commonly referred to as the Gibbs wave equation. Analysis of the dynamometer measurements can reveal a defective pump, leaking piping, insufficient balancing of the pumping unit, a partially clogged mud anchor, pump air lock, or an undersized pumping unit. The dynamometer diagram can be in the form of a graph, such as a dynamic graph.

[0043] Even if it was not the original artificial lift system of choice, rod pumping systems are often installed on many well types when productivity declines and the economics of the original system are undermined by higher operating costs. Therefore, rod pumping systems are likely to maintain their position as the commonly used artificial lift technology.

[0044] Figure 3 Also shown are surface condition graphs 370 and downhole condition graphs 390, which are load and distance graphs relative to time, for example, relative to graphs including Figure 2 210, 220, 230, and 240.

[0045] For the downhole condition diagram 390, as mentioned, it can be model-based. For example, the downhole forces can be estimated from the direct surface forces at the polished rod and the surface position measurements (and / or related measurements) by a mathematical model generally referred to as the Gibbs wave equation (e.g., "wave equation"). The wave equation describes the relationship between the surface and downhole forces acting on the rod and the position. Depending on the implementation, the wave equation can include various types of factors, such as the speed of sound in the rod, the elastic modulus of the rod material, the length of the rod string, the number of position increments, the number of time discretizations, the pump rate (e.g., cycles per minute, strokes per minute, etc.), the rod stroke length, the rod diameter, the specific gravity of the rod material, the dimensionless damping coefficient, the specific gravity of the fluid, the diameter of the pipe, etc.

[0046] Now refer to Figure 4 , shows a process 400 for determining a dynamometer model for a pump system 100 according to some embodiments. Figure 3As proposed, a dynamometer diagram is a force versus position graphical representation used in the oilfield industry (or other applicable industries) to assess the integrity of downhole displacement pump operations (e.g., the pump assembly 101 of the pump system 100). In some cases, the pump assembly 101 can be instrumented to determine the various defects mentioned above. However, in some cases, it may be expensive and impractical to instrument the pump assembly 101 due to the subsurface environment that defines the well 102 or otherwise surrounds the well 102. Therefore, the pump pressure and downhole pump position can be indirectly assessed based on the downhole forces acting on the pump plunger (e.g., the downhole forces on the plunger 116). In some embodiments, the downhole forces on the plunger 116 are estimated based on direct surface force measurements and direct position measurements (and / or related measurements) at the polished rod 146 using a mathematical model commonly referred to as the Gibbs wave equation.

[0047] In some embodiments, the Gibbs wave equation describes the relationship between (1) surface force measurements on the polished rod 146 and surface position measurements of the polished rod 146 and (2) downhole forces on the rod 144 and the downhole position of the rod 144 (e.g., a wellbore trajectory problem). Depending on the implementation, the Gibbs wave equation can solve the wellbore trajectory problem using a force or torque balance between factors involving the rod 144, such as Newtonian inertial forces, distributed elastic forces, solid friction, viscous damping forces, gravity, and buoyancy. Therefore, in order to solve the wellbore trajectory problem, it may be necessary to know the properties of the rod string 144 and the fluid properties of the pump assembly 101 (e.g., fluid interactions of the plunger 116 within the downhole pump 110, etc.). In some embodiments, the Gibbs wave equation can be applied to a vertical well (e.g., a well extending in a substantially one-dimensional vertical direction). For vertical wells, the Gibbs wave equation can be used to solve the wellbore trajectory problem by direct solution or by piecewise analytical solution based on the Fourier series of the acquired signals (e.g., direct surface force measurements and direct position measurements at the polished rod 146). Alternatively, a discretization solution proposed by the Everitt-Jennings algorithm can be used. For deviated wells (e.g., wells extending in various directions and dimensions outside the characteristics of a vertical well), applying the Gibbs wave equation to solve the wellbore trajectory problem can be more complex.

[0048] In some embodiments, the Gibbs wave equation can be estimated by the model. In other words, the model can be used to estimate (e.g., anticipate, model, predict, etc.) the calculation of the Gibbs wave equation as it will be used to solve the wellbore trajectory problem. Depending on the implementation, the model can be one-dimensional, two-dimensional, or three-dimensional in nature. In this sense, a one-dimensional model can anticipate the vertical movement of the rod string 144 (e.g., as an example, as shown in FIG. Figure 1The two-dimensional model can predict the forces and / or displacements of the pole 144 based on the one-dimensional model, where the horizontal forces and / or displacements (for example, as shown in FIG. Figure 1 Finally, the three-dimensional model can predict the forces and / or displacements of the column 144 based on the two-dimensional model, where the torsional forces and / or displacements and the abscissa forces and / or displacements (as an example, as shown in FIG. Figure 1 For the depicted post 144, twisting adds dimension as well as forward (eg, out of the page) and backward (eg, into the page).

[0049] As suggested above, the Gibbs wave equation can be solved for vertical wells in a relatively simple manner using a one-dimensional model. However, deviated wells may typically require a two-dimensional or three-dimensional model to accurately solve the wellbore trajectory problem using the Gibbs wave equation. Alternatively, the Gibbs wave equation for a deviated well can be solved using a one-dimensional model. However, this may require simplified estimates that require ignoring forces associated with multi-dimensional aspects, such as bending moments, buckling, and / or torsional stiffness of the rod string 144. Therefore, it would be advantageous to provide a solution to the Gibbs wave equation for a deviated well using a two-dimensional or three-dimensional model that provides a more accurate incorporation of the actual conditions associated with the deviated well. For example, such a solution may not only allow the bending moment and / or torsional stiffness characteristics of the rod string 144 to be properly accounted for, but may also allow the motion in all dimensions to be more accurately determined to model the buckling effects in the rod string 144.

[0050] In some embodiments, utilizing both two-dimensional and three-dimensional models of the Gibbs wave equation can each offer advantages over the other. On the one hand, a two-dimensional model may require less computation and overall bandwidth for a monitoring device such as controller 122. On the other hand, a three-dimensional model may require more computation and overall bandwidth for controller 122. For example, as noted above, a two-dimensional model may require three interrelated wave equations (structured to simulate the Gibbs wave equation) to identify vertical and horizontal forces and / or displacements associated with rod string 144. In contrast, a three-dimensional model may require six interrelated wave equations: the three aforementioned wave equations, further combined with three additional wave equations to identify abscissa forces and / or displacements, and torsional forces and / or displacements. Despite the additional computational requirements noted above, a three-dimensional model can certainly provide a more accurate Gibbs wave equation model for solving wellbore trajectory problems. Therefore, depending on the specific complexity of the wellbore deviation, available computational resources, and the like, a two-dimensional or three-dimensional model may be preferable. However, in general, both two-dimensional and three-dimensional models can each offer significantly increased computational complexity relative to a one-dimensional model. Regardless of the choice made between two-dimensional and three-dimensional models, solving the Gibbs wave equation therefrom may present practical challenges associated with the amount of time required for computation, numerical stability (e.g., uncertainty) challenges, etc. The systems and methods described herein may provide advantageous solutions to take advantage of the increased accuracy of solving wellbore trajectory problems using two-dimensional and / or three-dimensional models of the Gibbs wave equation, while also limiting (or otherwise eliminating) at least the above-mentioned challenges (if not other challenges) that are otherwise associated with using such models as opposed to one-dimensional models.

[0051] As discussed above, the Gibbs wave equation can be solved in a variety of ways based on the multiple dimensions depicted by the model of the Gibbs wave equation. However, as proposed above, it would be advantageous to provide systems and methods that not only utilize the improved accuracy associated with two-dimensional models and / or three-dimensional models, but also limit the side effects associated with increased computational requirements. Therefore, the systems and methods provided herein may involve a multi-stage process (as defined by process 400 below). For example, in a first stage (e.g., a "planning stage") of the implementation and / or operation of the pump system 100, it may be advantageous to utilize the advantages of the two-dimensional model and / or the three-dimensional model to determine a first model configured to solve the Gibbs wave equation. In this planning stage, the relationship between the surface conditions and the downhole conditions of the pump system 100 can be determined. In a second stage, the pump system 100 can then utilize one or more aspects of the first model (as described in more detail below) to identify a second model that is less complex and therefore more effective than the first model in other respects. For example, the first stage can be a planning stage (e.g., a stage primarily focused on providing the pump system 100 for a new well (e.g., well 102)). During this first phase, which involves the various expenses involved in constructing and implementing the pumping system in well 102, the accuracy of the Gibbs wave equation model may be crucial. Therefore, the second phase may be a "diagnostic phase" associated with the actual operation of pumping system 100 and determining downhole conditions in real time. During the second phase, the computational advantages gained with respect to the first model during the first phase may be exploited to a certain extent, although during the second phase, the emphasis may shift somewhat toward computational agility, thereby presenting greater advantages in a more streamlined model for solving the Gibbs wave equation, as described in more detail below.

[0052] Referring now more specifically to process 400, a "planning phase" for downhole dynamometer diagram estimation is initiated at process 401. As described in more detail below with reference to processes 402 through 410, the "planning phase" may involve a forward model for determining one or more impulse responses that describe one or more relationships between surface conditions and downhole conditions in a broad context. The forward model may apply assumed formation properties regarding various downhole force distributions, receive surface position values and downhole force distributions as inputs, and provide a force distribution along the rod 144 as output. Thus, the force distribution may include one or more impulse responses that may be used to operate the pump system during the diagnostic phase of actual operation.

[0053] At process 402, a ground position value can be simulated a priori by the controller 122 or any other computing system configured to simulate the conditions of the pump system 100. Although "ground position values" as used herein can be simulated for various moving components of the ground portion of the pump system 100 (e.g., counterweight 142, crank arm 134, beam 138, horse head 140, cable 142, etc.), in exemplary embodiments of the present disclosure, the ground position of the polishing rod 146 can be simulated to provide the systems and methods described herein. In some embodiments, measurements of the ground conditions of the pump system 100 can be obtained from actual ground position measurements and ground force measurements of the polishing rod 146. For example, the ground position of the polishing rod 146 can be detected by one or more position sensors of the pump system 100 (e.g., inclinometer 322, proximity switch 333 and / or other applicable sensors configured to detect the position of an object). The one or more position sensors of the pump system 100 can, in turn, provide a stable transmission of one or more position measurements of the polishing rod 146 to the controller 122. Thus, the controller 122 can compile at least one of the simulated or acquired steady-state surface position signals X(t) at a known sampling rate—the number of values simulated by the controller 122 or the measurements received by the controller 122 from one or more position sensors within a given time frame. In some embodiments, the time frame can be a standard measure of time, such as one second. In other embodiments, the controller can also determine the amount of time required for one movement cycle of the polishing rod 146 (e.g., moving from an initial point and returning to the initial point through one complete operating cycle of the pump system 100) and base the known sampling rate on this determined time frame. As described in more detail below, X(t) can be used as an input stimulus for one or more simulations of the pump system 100 using a forward model.

[0054] At each of process 403 and process 404, a forward model can be used to simulate the operation of the pump system 100. As discussed above, the forward model can be a two-dimensional model or a three-dimensional model configured to solve the Gibbs wave equation. In particular, the forward model can utilize parameters and observer techniques from control theory. For example, the forward model can include inputs that stimulate the pump system 100 (as simulated via the forward model) and outputs that can be measured. Typically, the input stimulus to the forward model can be a ground position value of the polishing rod 146 (e.g., a simulated or acquired ground position value X sf (t)) and the reference downhole force f dh (t). With X sf (t) On the contrary, in terms of actual measurement, f dh (t) may not be the acquired signal. Instead, a series of reference downhole force values may be applied as f dh(t), to determine the resulting estimated (eg, actual) downhole force f dh (t) and other variables involved in the operation of the pump system 100, as described in more detail below. Thus, the model used for the simulations involved in process 403 and process 404 can be "forward" in the sense that the output variable is first provided as an input variable in the form of preselected reference values for determining one or more relationships of the actual estimated output variable. Of course, f dh (t) can be used with X sf (t) is provided at the same state (e.g., over the same sequence of steady-state samples defined by the t values simulated or acquired in process 401).

[0055] In some embodiments, the simulations performed at process 403 and process 404 may be based on the dh In the case of process 402, the controller 122 can stimulate X via the input sf (t) and f dh (t) Perform a first simulation via the forward model, where f dh (t) = 0 (eg, the reference downhole force across t is zero). Then, at process 405, the pump system 100 may be simulated over a sequence of t values to determine a series of estimated surface force values F sf (t,0) (the first input variable is t, and the second input variable is f dh (t) = 0) and a series of estimated downhole position values X dh (t, 0). In the case of process 404, the controller 122 can use the forward model to calculate the stimulus X(t) and f dh (t) Perform the second simulation, where f dh (t) is the pulse load (f dh (t) = F pulse (t)). According to the implementation, F pulse (t) can be provided in a variety of formats, e.g. pulse (t) may be the expected load magnitude. Thus, at process 406, the controller 122 may determine two estimated value sequences F based on the second simulation. sf (t,F pulse (t)) and X dh (t,F pulse (t)).

[0056] At process 407, the controller 122 may determine whether the F sf (t,F pulse (t)) and F sfIn other words, at each value of t at which the pump system 100 is simulated by the first model and the second model, the values of F sf (t,F pulse Subtract F from (t) sf (t,0), to determine a series of values ΔF sf_p (t), where "p" is represented as an indication that the difference is generated based on system modeling using simulated or acquired ground position measurements X(t). Similarly, at process 408, the controller 122 may determine a similar indication at t X dh (t,F pulse (t)) and X dh (t,0) to similarly determine ΔX dh_p (t).

[0057] At processes 409 and 410, an impulse response is determined that relates the simulated or measured surface conditions of the pump system 100 (e.g., surface position values and surface force values for the polished rod 146) and the calculated downhole conditions of the pump system 100 (e.g., downhole position values and downhole force values for the rod 144). In general, an impulse response is the reaction of any dynamic system (e.g., calculated downhole conditions of the rod 144) in response to some external change (e.g., a change in the simulated or measured surface conditions for the polished rod 146). As described in more detail below, the impulse response can be used to estimate downhole force and downhole position values for the rod 144 based on the simulated or measured surface position and surface force values for the polished rod 146.

[0058] In some embodiments, the shape of the downhole pump load may be unknown. dh (t), it provides the transfer behavior of the rod 144. The transfer behavior of the rod 144 can be used to determine the first impulse response H F (τ). At process 409, it can be determined that ΔF sf_p (t) and F pulse (t) The first impulse response H F (τ). In some embodiments, the first impulse response H F (τ) is determined by expressing the relationship of these functions with respect to each other using a convolution function that converts the first impulse response H into F (τ) is combined into the first transfer function h F (τ). For example, h F (τ) and F pulse (t) can be expressed as the input of the first convolution function, where ΔF sf_p (t) is the output of the first convolution function. Usually, the convolution function is a function of two input functions (hF (τ) and F pulse (t-τ)) to produce the output function (ΔF sf_p (t)), and thus represents a function (ΔF sf_p How is the shape of (t) affected by another function (F pulse (t)). In other words, the first convolution function can indicate how the difference between the surface forces on the polished rod 146 (between a first simulation without a downhole force input stimulus and a second simulation with a downhole force input stimulus) changes based on changes in the downhole force input stimulus with respect to the rod 144. In such a convolution function, t is a constant, and τ is an integral variable used to determine the output of the convolution function. The first convolution function is provided below as an illustrative example.

[0059] ΔF sf_p (t) = conv(h F (τ),F pulse (t-τ))

[0060] In some embodiments, the F (τ) system identification process to determine the first impulse response H F (τ). For example, the transfer function h F (τ) can be expressed by the correlation function ΔF in the form of a vector sf_p (t) and F pulse (t-τ) can be expressed in matrix form, where F pulse (t-τ) is the input vector, and ΔF sf_p (t) is the output vector. The matrix can then be inverted (e.g., by inverting the correlation vector) to obtain H F (τ). In some embodiments, the first impulse response H F (τ) may be a Hankel matrix, which may include the impulse response as the downhole force F dh (t) Differential force with the ground ΔF sf_p The following convolution function is provided below as an illustrative example.

[0061] ΔF sf_p (t) = conv(h F (τ),F dh (t))=H F (τ)F dh (t)

[0062] In some embodiments, deconvolution is performed to determine the downhole force F dh (t) = H -1 F(τ)ΔF sf_p(t). For example, in some embodiments, the pseudo-inverse matrix H -1 F (τ) is implemented with regularization. As an example, a direct inversion process can be used. As another example, a direct inversion process with regularization can be used. As another example, a Wiener filter can be applied to invert the matrix. As yet another example, Tikhonov regularization can be applied to invert the matrix. As yet another example, the inversion can be solved in real time with a direct solver. In one example, a selection of regularization parameters can be applied, for example, selecting regularization as a relatively small portion of a relatively large eigenvalue. For example, the matrix can first be transformed into a diagonal form, a regularization value can be added when the eigenvalue is below a threshold, and then an inverse transformation from the diagonal form can be performed. In one example, the inversion problem can be solved as a minimum search optimization problem. For example, a least squares solution can be applied, and the minimization problem of minimizing the quadratic error can also be solved by a gradient descent method or a conjugate gradient method.

[0063] At process 410, it is determined that ΔX dh (t) and F pulse (t) The associated second impulse response H X (τ). Similar to process 409, H X (τ) is determined by expressing the relationship of these functions with respect to each other using a convolution function that converts the first impulse response H into X (τ) is combined into the first transfer function h X (τ). The second convolution function may indicate how the downhole force input stimulus varies based on the difference between the estimated downhole positions (between a first simulation without the downhole force input stimulus and a second simulation with the downhole force input stimulus). The second convolution function is provided in the following illustrative example, H X (τ) can be expressed similarly to H as discussed above. F (τ) is determined (e.g., by the inversion of the matrix, where ΔX dh_p (t-τ) is the input vector, and F pulse (t-τ) is the output vector).

[0064] F pulse (t) = conv(h X (τ),ΔX dh_p (t-τ))

[0065] At process 411, a "diagnostic phase" may be initiated, which applies h F (τ) and h X(τ) to determine downhole force and position estimates (e.g., downhole conditions) about the polished rod 146 based on the measured force and position values (e.g., surface conditions) about the polished rod 146. The diagnostic phase can be characterized as described below with reference to processes 412 through 417. Depending on the implementation, the planning phase can be used for monitoring and control situations during actual operation of the pump system 100.

[0066] At process 412, ground position measurements and ground force measurements are obtained by controller 122. Compared to the ground position measurements simulated (or obtained) by controller 122 with reference to process 402, the ground position measurements of polished rod 146 obtained at process 412 can be used in real time to determine the downhole position and force values of rod 144, as described in more detail below. As described above with reference to process 401, the ground position measurements can be simulated (or obtained by a position sensor of pump system 100), and controller 122 can compile the simulated (or obtained) steady-state ground position signal X2(t) at a known sampling rate. The ground force value can indicate the load on polished rod 146 (e.g., the load on the ground portion of rod 144). When the ground force measurements are obtained from the actual ground conditions of pump system 100, the ground force measurements can be detected by one or more load sensors in pump system 100 (e.g., load cell 334, current sensor 335, beam transducer 336, and / or other applicable sensors configured to detect the load on the object). The one or more load sensors of the pump system 100 may, in turn, provide a steady transmission of one or more force measurements on the polished rod 146 to the controller 122. Thus, the controller 122 may compile a simulated or acquired steady-state ground force signal F(t) at a known sampling rate.

[0067] At process 413, the ground position signal X2(t) and the ground force signal F(t) are synchronized with the ground position signal X1(t) (e.g., the ground position signal simulated or acquired at process 401 during the planning phase). For example, for each of X2(t) and F(t), the signal phase associated therewith may be adjusted (e.g., shifted) to scale and match the signal phase associated with X1(t).

[0068] At process 414, the controller 122 determines the synchronized ground force value F(t) across time (t) and the ground force value F sf The difference ΔF between (t, 0) (the estimated force value determined at process 405 based on the simulation of the pump system 100, where the reference downhole force at process 403 is zero) SF (t,F DH ). ΔF SF It is described in detail here as F DHfunction (with 0 or F from the simulation described above with reference to process 403 to process 406) pulse (t) opposite), because ΔF SF It is considered that the “actual” downhole force F is currently unknown. DH is a function of the downhole force (0 and F) and will be calculated as described below, rather than via the reference downhole force (0 and F pulse (t)) to assume.

[0069] At process 415, the impulse response H is now F (τ) (e.g., as described above with reference to process 409, based on ΔF sf_p (t) and F pulse (t) Correlation calculation between ) applied to ΔF SF (t,F DH ) to estimate the actual downhole force F mentioned above DH (t).

[0070] At process 416, the impulse response H X (τ) (e.g., as described above with reference to process 410, based on ΔX dh_p (t) and F pulse (t) is applied to the correlation between ΔX SF (t,X DH ), similarly estimate the actual downhole position value X DH (t).

[0071] At process 417, referring to the estimated actual downhole position value X DH (t) (see process 415) and the estimated actual downhole force value F DH (t) (see process 416), mapping the acquired ground position measurement X2(t) and the acquired ground force measurement F(t) (see process 412) to generate a map of X2(t) and F(t) with respect to X across time scale t. DH (t) and F DH (t) Related indicator diagram.

[0072] As described herein, according to some embodiments, the pump system 100 can implement one or more offline techniques and one or more online or real-time techniques to generate a digital twin. A digital twin can be an instantiation of one or more reduced-order models (ROMs) that digitally encapsulates the necessary model properties as a system across the intended operating space and can include design, installation, and model variables. A digital twin can be an instantiation of a ROM at a specific point in time and can operate in real time based on measurements and / or real-time information (e.g., real-time inputs). The digital twin can output real-time outputs of any ROM included in the digital twin. The digital twin can be implemented as one of the real-time technologies of the pump system 100, using real-time inputs (e.g., sensor data, measurements, etc.) and outputting real-time outputs (e.g., predicted values of one or more variables of the system, calculated values of one or more variables of the system, values of calibrated variables of the system, etc.). The digital twin can be configured to estimate or predict values of variables that are relatively more difficult to measure, such as gas content, inlet pressure, damping, etc. It should be understood that these specific variables that are more difficult to measure are presented as examples and should not be construed as limiting. According to one embodiment, a digital twin can be implemented for Figure 4 In some embodiments, the ROM may be an interpolated tensor reduced order model (tROM).

[0073] In some embodiments, the method 400 may utilize a machine learning model. For example, the planning phase or learning phase of the method 400 may be implemented in two main steps: (i) calculating the impulse response H F (τ), H X (τ); and (ii) using the impulse response H based on input parameters (e.g., at least one or more of density, damping, or viscosity, etc.) F (τ), H X In some embodiments, the pump system 100 and / or method 400 can perform both steps of the planning phase or the learning phase in a single step using a recurrent neural network (e.g., a recursive neural network). dh (t) = F pulse (t) Excitation simulation within a range of operating parameters and speeds, to obtain a single impulse response H associated with that range F (τ), H X (τ) is calculated, for example, as a learning sample for regression. In some embodiments, a recursive form of the dynamic equation can be obtained, which can be further used for deconvolution in subsequent runtime steps of the diagnostic phase of method 400. For example, the impulse response H F (τ), H XThe learning samples of (τ) can be used to develop a regression model that facilitates the impulse response H under the estimated and measured operating parameters in real time at the well site. F (τ), H X Calculation of (τ).

[0074] In some embodiments, during the diagnostic phase of the workflow for a hydrocarbon, oil or petroleum system or any other device of the pump system 100, ground values such as the force F may be used initially. sf (t) and position X sf (t). These ground values can be used to determine estimates of damping, density Rho, and friction coefficient, as well as initial estimates of other relevant parameters of the pump system 100. In some embodiments, the dynamometer prediction model can be based on simulated learning samples. In some embodiments, the dynamometer prediction model can be implemented by interpolating using, for example, a lookup table. Additionally, in some embodiments, Gaussian or neural network regression can be utilized.

[0075] In some embodiments, a linearization based on the operating point and Figure 4 The method automatically tunes the parameters of the prediction. The regression model can be trained using pre-existing well data and simulated well data. The output of the first regression model can then be used as the input of the regression model to predict the downhole force f dh (t) Differential force with the ground ΔF sf_p The first impulse response H between (t) F (τ) (for the simulated no-load condition) and the downhole force F dh (t) and downhole position X dh (t) The impulse response H X (τ) (relative to a simulated no-load condition at the same operating point). Additional regression models can be used to estimate the no-load curve (eg, the curve without load) as a function of the operating point.

[0076] In some embodiments, the impulse response H F (τ) can be deconvolved with the ground differential force ΔF sf_p (t) to identify the downhole force estimate F dh (t), and through convolution with the estimated value F dh (t) to determine the estimated downhole position X dh (t). Using these estimates F dh (t) and X dh (t), a reconstruction of the downhole dynamometer diagram can be created.

[0077] In one embodiment, the dynamometer diagram can be used in a multi-color image (such as, for example, including two colors) for a regression model to predict gas content and inlet pressure. Optionally or alternatively, a third color can also be used to include a measured ground dynamometer diagram. The same or substantially the same image can also be used in a classification model.

[0078] In some embodiments, convolutional neural networks (CNNs) can be used for regression, auto-tuning, and Figure 4 Parameter estimation is performed using the proposed method. Each model's learning sample database can also be supplemented with generic dynamometer data from other wells to increase the regression and classification learning sample database. This labeled data can be used for supervised learning; unlabeled data can be used for semi-supervised learning. To achieve automatic tuning, the forward model is run multiple times with different well parameters to find the closest match to the expected downhole dynamometer diagram based on the pump parameters.

[0079] In some embodiments, deconvolution can be performed by at least one of the following two methods: (i) testing conjugate gradient method and (ii) pre-computed Tikhonov regularization. In some embodiments, an initial regression model can be tested with a CNN, which can be retrained with the latest data and / or supplemented with unscaled and / or normalized data (e.g., unscaled and / or normalized data of ground force values). In some embodiments, the subsequent regression model can be a regression-based tROM; for example, the resolution obtained according to this method can be of higher quality for relatively deep wells. In some embodiments, the final regression model and / or classification model can be tested with a CNN, retrained with the latest data, and / or supplemented with unscaled and / or normalized data. In some embodiments, the classification model can be a semi-supervised learning CNN.

[0080] In some embodiments, the surface dynamometer diagram can also be supplemented with a surface pressure dynamometer diagram in a multi-color image, such as the surface pipeline pressure p(xsf) with respect to the surface position value or measurement result. Although a convolutional neural network is described herein for the dynamometer diagram model, any other regression and classification model can also be used.

[0081] In some embodiments, by utilizing aspects of machine learning, including but not limited to those described below, rapid SRP downhole dynamometer diagram estimation for deviated wells can be achieved. A dynamometer diagram can be embodied as a force-position diagram used in the oilfield industry to assess the operational integrity of downhole displacement pumps. The primary focus is the pumped gas content relative to the pump pressure of a specific system. Instrumentation for direct pump position and pressure measurements is often expensive and impractical. Therefore, in SRP, pump pressure and position are estimated indirectly based on downhole forces acting on the pump plunger. Downhole forces are estimated based on direct surface force and position measurements or related measurements at the polished rod using a mathematical model, often referred to as the Gibbs wave equation in some embodiments. The wave equation describes the relationship between surface and downhole forces acting on the rod and position. It can be solved in a variety of ways. During the planning phase, a forward model can be used. Based on assumed formation properties, various downhole force distributions can be considered. The downhole force distribution and surface motion are inputs to the forward model. The output of the forward model is the force distribution along the rod string, which is primarily used to accurately determine rod string dimensions.

[0082] For in-operation monitoring and control, different solutions of the wave equation, also known as diagnostic solutions, are used. In this case, the inputs to the solution of the wave equation are surface position and forces, and the outputs are downhole position and forces. In some embodiments, a fast and robust solution can be provided based on an initial simulation solution of a forward model in the operating point of the monitored well derived from surface position measurements. The relationship between the surface signal and the downhole signal simulation results is then approximated using a simpler dynamic model and its inverse model. As long as the operating point does not change drastically, the inverse solution of the dynamic model approximation allows, in some embodiments, the calculation of downhole forces and positions quickly enough for assessing pump health and for dynamic control.

[0083] Reference Figure 5 9, a method that can be used as a process 400 ( Figure 4 ) and can be used with SRP. Figure 5, a recurrent neural network (RNN) implements the relationship between downhole and surface predictions, measurements, or properties. SRP process 500 includes model 502, model 504, model 506, and model 508. Model 502 is a predictive surface dynamometer regression model that receives a periodic input of surface forces represented by the function F_sf(x_sf) and provides predictions of Rho Eta and Fr based on simulated learning samples. Model 504 is a predictive tROM model that receives a periodic input of surface forces represented by the function F_sf(t) and predictions of Rho Eta and Fr from model 502 and provides results based on the function h(t, Eta, Rho, fr). In some embodiments, model 504 uses interpolation with a lookup table. In some embodiments, Gaussian or neural network (NN) regression can be used in model 504.

[0084] Model 506 receives the surface force represented by the function F_sf(t) and the position represented by the function x_sf(t), as well as the impulse response or result from model 504, and provides downhole force results and downhole position results represented by the corresponding functions f_dh(t) and x_dh(t). Model 506 is a deconvolution model. In some embodiments, model 506 can be eliminated and, in some embodiments, replaced by an RNN prediction. Model 508 receives the surface force represented by the function F_sf(x) and the downhole force represented by the function f_dh(t), and provides an alert or classification as well as gas content, Rho, and inlet pressure. Model 508 is a dynamometer model and, in some embodiments, uses simulation learning. In some embodiments, a convolutional neural network (CNN) model 512 can replace models 502 and 404, and a recurrent neural network (RNN) model 514 can replace model 506. Model 512 receives the surface force represented by the function F_sf(t) and the position represented by the function x_sf(t) and provides an impulse response or result. Model 514 receives the surface force represented by the function F_sf(t) and the position represented by the function x_sf(t) and the impulse response or result from model 504 and provides a downhole force result and a downhole position result represented by the corresponding functions f_dh(t) and x_dh(t).

[0085] Reference Figure 6 , recurrent NN training can utilize process 600, which accesses a simulation database of values including, but not limited to: surface force (F_sf), surface position (X_sf), downhole force (F_dh), gas content, Rho, Eta, fr, inlet pressure (pi), etc. RNN training operation 602 is used to provide RNN model 604, which can be used as model 514 ( Figure 5In some embodiments, the training operation 602 uses physical model parameters specific to a particular well. The parameters may include fixed physical parameters and time-varying parameters.

[0086] Reference Figure 7 , a regression model can be used that directly predicts the design parameters using the dynamometer diagram. NN model 702 receives ground force, ground position, and SRP model parameters (e.g., trajectory, rod cross-section, stiffness diameter, etc.), and provides Rfo, Eta, fr, gas charge, and inlet pressure. Model 702 does not require a dynamic model, has lower complexity, and requires less understanding of the underlying physics. Model 702 can be any regression model.

[0087] Reference Figure 8 , training can utilize process 800, which accesses a simulated database of values including, but not limited to: surface force (F_sf), surface position (X_sf), downhole force (F_dh), gas content, Rho, Eta, fr, inlet pressure (pi), etc. The training operation 802 is used to provide a regression model 804, which in some embodiments can be used as the model 504 ( Figure 5 ). Model 802 may be model 702 formed using training operation 802. In some embodiments, training operation 802 uses physical model parameters specific to a particular well. The parameters may include fixed physical parameters and parameters that vary over time. In some embodiments, model 704 uses parameters that, in some embodiments, vary over time after operation 802.

[0088] Configuration of the Exemplary Embodiment

[0089] As used herein, the terms "approximately," "about," "substantially," and similar terms are intended to have a broad meaning consistent with common and accepted usage by persons of ordinary skill in the art to which the subject matter of this disclosure belongs. Those skilled in the art reading this disclosure should understand that these terms are intended to allow description of certain features described and claimed without limiting the scope of such features to the precise numerical ranges provided. Accordingly, these terms should be interpreted as indicating that insubstantial or inconsequential modifications or alterations to the subject matter described and claimed are considered to be within the scope of this disclosure as set forth in the appended claims.

[0090] It should be noted that the term "exemplary" and variations thereof, as used herein to describe various embodiments, are intended to indicate that such embodiments are possible examples, representations, or illustrations of possible embodiments (and such terms are not intended to imply that such embodiments are necessarily unusual or best examples).

[0091] As used herein, the term "coupling" and variations thereof refer to the direct or indirect engagement of two components with one another. Such engagement may be stationary (i.e., permanent or fixed) or removable (i.e., removable or releasable). Such engagement may be achieved by coupling the two components directly to one another, by coupling the two components to one another using a separate intermediate component and any additional intermediate components coupled to one another, or by coupling the two components to one another using an intermediate component that is integrally formed with one of the two components to form a single, one-piece body. If "coupling" or variations thereof are modified by additional terms (i.e., directly coupled), the general definition of "coupling" provided above is modified by the plain language meaning of the additional terms (i.e., "directly coupled" means that the two components engage without any separate intermediate component), resulting in a narrower definition than the general definition of "coupling" provided above. Such coupling may be mechanical, electrical, or fluidic.

[0092] As used herein, the term "or" is used in its inclusive sense (and not in its exclusive sense), such that when used to connect a list of elements, the term "or" means one, some, or all of the elements in the list. Unless specifically stated otherwise, connective language such as the phrase "at least one of X, Y, and Z" is understood to express that the element can be: any one of X, Y, and Z; X and Y; X and Z; Y and Z; or X, Y, and Z (i.e., any combination of X, Y, and Z). Thus, unless otherwise specified, such connective language is generally not intended to imply that certain embodiments require that at least one of X, at least one of Y, and at least one of Z each be present.

[0093] References herein to the positions of elements (i.e., "top," "bottom," "above," "below") are intended only to describe the orientations of the various elements in the drawings. It should be noted that according to other exemplary embodiments, the orientations of the various elements may differ, and such variations are intended to be encompassed by the present disclosure.

[0094] Although the drawings and description may illustrate a particular order of method steps, the order of such steps may differ from that depicted and described, unless otherwise specified above. Two or more steps may also be performed simultaneously or partially simultaneously, unless otherwise specified above. Such variations may depend, for example, on the software and hardware systems selected and the designer's preferences. All such variations are within the scope of the present disclosure.

[0095] It is important to note that the construction and arrangement of the devices shown in the various exemplary embodiments are illustrative only. In addition, any element disclosed in one embodiment can be combined or used with any other embodiment disclosed herein. Although only one example of an element from one embodiment that can be combined or used with another embodiment is described above, it should be appreciated that other elements of the various embodiments can be combined or used with any other embodiment disclosed herein.

Claims

1. A pump system comprising a pump disposed in a well, an actuator operable to move a rod, and a controller, the rod comprising a surface end coupled to the actuator and a downhole end coupled to the pump, the controller being configured to: A first impulse response and a second impulse response associated with the pump system are identified, wherein The identification includes: simulating a first set of position data associated with the ground end of the pole; generating, based on a first model of the pump system and the position data, a first set of data associated with simulated operation of the pump system with a load stimulus and a second set of data associated with simulated operation of the pump system without the load stimulus, wherein the first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data; Generating a second model of the pump system, wherein generating the second model of the pump system comprises: measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values for a downhole condition of the rod based on the identified first impulse response, the force data, and the position data; estimating one or more position values of a downhole condition of the rod based on the identified second impulse response and the one or more force values; and The pump system is operated based on the second model.

2. The system according to claim 1, wherein: The second model is an indicator diagram.

3. The system according to claim 1, wherein: The first model is a two-dimensional model of the rod.

4. The system according to claim 1, wherein: The first model is a three-dimensional model of the rod.

5. The system according to claim 1, wherein: Comparison of the first set of data and the second set of data identifies differences in surface force values and differences in downhole position values between the first set of data and the second set of data.

6. The system according to claim 5, wherein: Identifying the first impulse response and the second impulse response further includes: identifying a first transfer function relating the difference in ground force values to the load stimulus; determining the first impulse response based on the first transfer function; identifying a second transfer function relating the difference in downhole position values to the load stimulus; and The second impulse response is determined based on the second transfer function.

7. The system according to claim 6, wherein: Determining the first impulse response based on the first transfer function includes: expressing the first transfer function as a first matrix based on a first vector of differences in the ground force values and a second vector of the load stimulus values, and wherein determining the second impulse response based on the second transfer function includes: expressing the second transfer function as a second matrix based on a third vector of differences in the downhole position values and the second vector of the load stimulus values.

8. A method of controlling a pump system comprising a pump disposed in a well and an actuator operable to move a rod, the rod comprising a surface end coupled to the actuator and a downhole end coupled to the pump, the method comprising: Identifying a first impulse response and a second impulse response associated with the pump system, wherein the identifying comprises: simulating a first set of position data associated with the ground end of the pole; generating, based on a first model of the pump system and the position data, a first set of data associated with simulated operation of the pump system with a load stimulus and a second set of data associated with simulated operation of the pump system without the load stimulus, wherein the first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data; Generating a second model of the pump system, wherein generating the second model of the pump system comprises: measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values for a downhole condition of the rod based on the identified first impulse response, the force data, and the position data; estimating one or more position values of a downhole condition of the rod based on the identified second impulse response and the one or more force values; and The pump system is operated based on the second model.

9. The method according to claim 8, wherein The second model is: a dynamometer diagram, a regression model or a neural network model; includes the dynamometer diagram, the regression model or the neural network model; or is a part of the dynamometer diagram, the regression model or the neural network model.

10. The method according to claim 8, wherein The first model is a two-dimensional model of the rod.

11. The method according to claim 8, wherein The first model is a three-dimensional model of the rod.

12. The method according to claim 8, wherein Comparison of the first set of data and the second set of data identifies differences in surface force values and differences in downhole position values between the first set of data and the second set of data.

13. The method according to claim 12, wherein: Identifying the first impulse response and the second impulse response further includes: identifying a first transfer function relating the difference in ground force values to the load stimulus; determining the first impulse response based on the first transfer function; identifying a second transfer function relating the difference in downhole position values to the load stimulus; and The second impulse response is determined based on the second transfer function.

14. The method according to claim 13, wherein: Determining the first impulse response based on the first transfer function includes: expressing the first transfer function as a first matrix based on a first vector of differences in the ground force values and a second vector of the load stimulus values, and wherein determining the second impulse response based on the second transfer function includes: expressing the second transfer function as a second matrix based on a third vector of differences in the downhole position values and the second vector of the load stimulus values.

15. A controller for controlling a pump system, comprising: in, The pump system includes a pump disposed within a well and an actuator operable to move a rod, the rod including a surface end coupled to the actuator and a downhole end coupled to the pump, wherein the controller includes one or more processors and a memory, the one or more processors being configured to: Identifying a first impulse response and a second impulse response associated with the pump system, wherein the identifying comprises: simulating a first set of position data associated with the ground end of the pole; generating, based on a first model of the pump system and the position data, a first set of data associated with simulated operation of the pump system with a load stimulus and a second set of data associated with simulated operation of the pump system without the load stimulus, wherein the first impulse response and the second impulse response are based on a comparison of the first set of data and the second set of data; Generating a second model of the pump system, wherein generating the second model of the pump system comprises: measuring a second set of position data and a set of force data associated with the rod during operation of the pump system; estimating one or more force values for a downhole condition of the rod based on the identified first impulse response, the force data, and the position data; estimating one or more position values of a downhole condition of the rod based on the identified second impulse response and the one or more force values; and The pump system is operated based on the second model.

16. The controller according to claim 15, wherein: The first model is a two-dimensional model of the rod.

17. The controller according to claim 15, wherein: The first model is a three-dimensional model of the rod.

18. The controller according to claim 15, wherein: Comparison of the first set of data and the second set of data identifies differences in surface force values and differences in downhole position values between the first set of data and the second set of data.

19. The controller according to claim 18, wherein: Identifying the first impulse response and the second impulse response further includes: identifying a first transfer function relating the difference in ground force values to the load stimulus; determining the first impulse response based on the first transfer function; identifying a second transfer function relating the difference in downhole position values to the load stimulus; and The second impulse response is determined based on the second transfer function.

20. The controller according to claim 19, wherein Determining the first impulse response based on the first transfer function includes: expressing the first transfer function as a first matrix based on a first vector of differences in the ground force values and a second vector of the load stimulus values, and wherein determining the second impulse response based on the second transfer function includes: expressing the second transfer function as a second matrix based on a third vector of differences in the downhole position values and the second vector of the load stimulus values.

21. A controller for controlling a pump system, the pump system comprising a pump arranged for use at a well, wherein The controller includes one or more processors and memory, the one or more processors being configured to: providing a first impulse response in response to a surface position input associated with the pump and a surface load input associated with the pump using a first model, the first model being a neural network; providing a downhole position associated with the pump and a downhole load associated with the pump using a second model in response to a surface position input associated with the pump and a surface load input associated with the pump and the first impulse response, the second model being a regression model or a neural network model; The pump system is operated using the second model.

22. A controller for controlling a pump system, the pump system comprising a pump arranged for use at a well, wherein The controller includes one or more processors and memory, the one or more processors being configured to: providing a downhole position associated with the pump and a downhole load associated with the pump in response to a surface position input associated with the pump and a surface load input associated with the pump using a model, the model being a regression model or a neural network model trained using well-specific data; and The pump system is operated using the second model.

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