EP2963234A1 - Stressberechnungen für saugstangen-pumpensysteme - Google Patents

Stressberechnungen für saugstangen-pumpensysteme Download PDF

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Publication number
EP2963234A1
EP2963234A1 EP15174273.1A EP15174273A EP2963234A1 EP 2963234 A1 EP2963234 A1 EP 2963234A1 EP 15174273 A EP15174273 A EP 15174273A EP 2963234 A1 EP2963234 A1 EP 2963234A1
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EP
European Patent Office
Prior art keywords
rod
stress
finite difference
sucker rod
string
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Granted
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EP15174273.1A
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English (en)
French (fr)
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EP2963234B1 (de
Inventor
Victoria Pons
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Weatherford Technology Holdings LLC
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Weatherford Lamb Inc
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E21B47/008—Monitoring of down-hole pump systems, e.g. for the detection of "pumped-off" conditions
    • E21B47/009—Monitoring of walking-beam pump systems
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/12—Methods or apparatus for controlling the flow of the obtained fluid to or in wells
    • E21B43/121—Lifting well fluids
    • E21B43/126—Adaptations of down-hole pump systems powered by drives outside the borehole, e.g. by a rotary or oscillating drive
    • E21B43/127—Adaptations of walking-beam pump systems

Definitions

  • aspects of the present disclosure generally relate to hydrocarbon production using artificial lift, and, more particularly, to a technique for stress calculations at any depth for sucker rod pumping systems.
  • a wellbore is drilled into the earth to intersect a productive formation.
  • pumps can be used in wells to help bring production fluids from the productive formation to a wellhead located at the surface. This is often referred to as providing artificial lift, as the reservoir pressure may be insufficient for the production fluid to reach the surface on its own (i.e., natural lift).
  • An oil well generally comprises a casing, a string of smaller steel pipe inside the casing and generally known as the tubing, a pump at the bottom of the well, and a string of steel rod elements, commonly referred to as sucker rods, within the tubing and extending down into the pump for operating the pump.
  • Various devices as are well known in the art are provided at the top of the well for reciprocating the sucker rod to operate the pump.
  • aspects of the present disclosure generally relate to hydrocarbon production using artificial lift, and, more particularly, to a technique for stress calculations at any depth for sucker rod pumping systems.
  • a method for determining stress along a sucker rod string disposed in a wellbore generally includes receiving, at a processor, measured rod displacement and rod load data for the sucker rod string, wherein the sucker rod string comprises a plurality of sections; and calculating stress values at a plurality of finite difference nodes for at least one of the plurality of sections based, at least in part, on the measured rod displacement and rod load data.
  • the system generally includes a sucker rod string comprising a plurality of sections disposed in a wellbore ; at least one sensor configured to measure rod displacement of the sucker rod string ; at least one sensor configured to measure rod loading of the sucker rod string ; and a processor configured to calculate stress values at a plurality of finite difference nodes for at least one of the plurality of sections based, at least in part, on the measured rod displacement and rod load data.
  • the computer readable medium generally includes computer executable code stored thereon for receiving measured rod displacement and rod load data for a sucker rod string, wherein the sucker rod string comprises a plurality of sections; and calculating stress values at a plurality of finite difference nodes for at least one of the plurality of sections based, at least in part, on the measured rod displacement and rod load data.
  • the one or more aspects comprise the features hereinafter fully described and particularly pointed out in the claims.
  • the following description and the annexed drawings set forth in detail certain illustrative features of the one or more aspects. These features are indicative, however, of but a few of the various ways in which the principles of various aspects may be employed, and this description is intended to include all such aspects and their equivalents.
  • aspects of the present disclosure provide techniques for stress calculations for sucker rod pumping systems. This may allow well operators to accurately monitor the pump fillage and control the pump accordingly.
  • a reciprocating rod lift system 100 e.g., sucker-rod pump system or rod pumping lift system
  • sucker-rod pump system or rod pumping lift system such as that depicted in FIG. 1
  • FIG. 1 The production of oil with a reciprocating rod lift system 100 (e.g., sucker-rod pump system or rod pumping lift system), such as that depicted in FIG. 1 , is common practice in the oil and gas industry.
  • FIG. 1 illustrates a reciprocating rod lift system 100 with a control unit 110 (e.g., including a rod pump controller or variable speed drive controller) for controlling the rod pump in an effort to extract fluid from a well, according to certain aspects of the present disclosure.
  • a control unit 110 e.g., including a rod pump controller or variable speed drive controller
  • the reciprocating rod lift system 100 may employ any suitable pumping unit.
  • the reciprocating rod lift system 100 is driven by a motor or engine 120 that turns a crank arm 122. Attached to the crank arm 122 are a walking beam 124 and a horsehead 101. A cable 126 hangs off the horsehead 101 and is attached to a sucker rod 102 (e.g., a string of steel rod elements or a continuous rod string). The sucker rod 102 is attached to a downhole rod pump 104 located within the wellbore 128. In operation, the motor 120 turns the crank arm 122 which reciprocates the walking beam 124 which reciprocates the sucker rod 102.
  • the rod pump 104 consists of a pump barrel 106 with a valve 114 (the "standing valve") located at the bottom that allows fluid to enter from the wellbore, but does not allow the fluid to leave.
  • the pump barrel 106 can be attached to or part of the production tubing 130 within the well bore 128.
  • Inside the pump barrel 106 is a close-fitting hollow plunger 116 with another valve 112 (the “traveling valve") located at the top. This allows fluid to move from below the plunger 116 to the production tubing 130 above and does not allow fluid to return from the tubing 130 to the pump barrel 106 below the plunger 116.
  • the plunger 116 may be moved up and down cyclically by the horsehead 101 at the surface via the sucker rod 102, where the motion of the pump plunger 116 comprises an "upstroke” and a "downstroke,” jointly referred to as a "stroke.”
  • a polished rod 118 which is a portion of the rod string passing through a stuffing box 103 at the surface, may enable an efficient hydraulic seal to be made around the reciprocating rod string.
  • a control unit 110 which may be located at the surface, may control the system 100.
  • the reciprocating rod lift system 100 is designed with the capacity to remove liquid from the wellbore 128 faster than the reservoir can supply liquid into the wellbore 128.
  • the downhole pump does not completely fill with fluid on every stroke.
  • the well is said to be “pumped-off” when the pump barrel 106 does not completely fill with fluid on the upstroke of the plunger 116.
  • the term "pump fillage” is used to describe the percentage of the pump stroke which actually contains liquid.
  • rod-pump systems e.g., reciprocating rod lift system 100
  • rod-pump systems can reduce the bottom hole pressure to a "near zero" value.
  • the foremost goal of rod pumping optimization is to match well displacement to inflow, which may be difficult if inflow is unknown or highly uncertain. Uncertainty related to inflow may lead to an overly conservative approach, for example, where the system is designed or operated such that the pump displacement is lower than the inflow, such as by continuous pumping. In this case, the rod lift system runs without any problem and is sometimes referred to as "optimized" operation, although the well production is usually suboptimal and losing revenue.
  • uncertainty related to inflow may lead to an overly aggressive approach, for example, where the system is designed or operated such that the pump displacement is higher than the inflow, such as by intermittent pumping.
  • the downhole pump and rod lift system suffers from issues such as fluid pound, pump-off, gas interference, and correspondingly higher failure rates due to incomplete pump fillage.
  • the rod string 102 may be a straight string or a tapered string.
  • a tapered string includes multiple sections (e.g., "tapers") having varying diameters. Each section, or taper, may include a plurality of rod elements.
  • stress is only computed at the top of each taper; however, stress failures occur in areas of high friction and stress, which may not be near the top of the taper and, therefore, may be undetected by traditional stress computations.
  • Stress may be defined as a material's internal resistance per unit area when an external load is applied to it. Stress analysis is the practice of evaluating the stress distribution within a given material. In a rod string (e.g., such as rod string 102) subjected to axial tension, stress analysis may involve computing the average normal stress. In the ideal case, the rod string can be considered prismatic, for example, similar to a straight bar whose cross-section is uniform throughout its length. Although, in practice, a rod string may not be prismatic.
  • the yield strength of a material may be defined as the amount of stress at which the material will begin to undergo plastic deformation.
  • the tensile strength of a material may be defined as the maximum stress the material can withstand, due to pulling or stretching, before the material fails or breaks. Even though the load applied to a component is usually well below the yield strength of the material the component is made of, the component may eventually fail through many repeated loads. For example, a small amount of damage may be done to the component with each cycle which, alone, may be insufficient to cause the component to fail, but over repeated cycles may accumulate and eventually cause a fatigue failure of the component.
  • the service factor is a factor used to account for the corrosiveness of the environment.
  • the value for the service factor is typically found between zero and one, although in some case the service factor may be greater than one.
  • Yield strength and tensile strength may be known quantities, and therefore, for a rod string operating under normal conditions, the lifetime for that rod string may be known or predetermined.
  • the normal conditions may be ideal conditions rather than actual conditions. Instead, failures and rod life may be anticipated by closely monitoring the behavior of the stress function with respect to each other throughout the rod string. Some sections of the rod string may be more sensitive than others and, therefore, a more detailed and in-depth analysis may be used for those sections.
  • Sucker-rod pumps may experience two types of failures: tensile failures and fatigue failures.
  • a tensile failure may occur when the sucker rod is over-stressed, for example, when the force exerted on the sucker rod material results in an axial pulling force overcoming the tensile strength of the material. For example, if excessive pull is applied to the sucker rod, the rod stress may exceed the rod material tensile strength causing a tensile break.
  • Tensile failures typically occur in the rod body, where the cross-sectional area may be the smallest. Tensile failures may materialize as a permanent stretch and/or small breaks in the sucker rod. Once the sucker rod has incurred tensile failures, if the sucker rod is run again, the failure points may become stress raisers since the load bearing cross-sectional area is reduced.
  • static loads may be tensile loads
  • fatigue failures may occur from repeated load variations within the rod string.
  • the rod load is equal to the rod weight
  • the rod load is equal to the rod weight and the fluid load.
  • the fluid load represents an alternating stress, which may lead to fatigue damage and/or failure.
  • Sucker rod failures are typically attributed to fatigue breaks, which may occur at stress levels well below the ultimate tensile strength or even below the yield strength of the sucker rod (e.g., made of steel material having a high tensile strength). Repeated stresses cause material fatigue or plastic tensile failure of the sucker rod. The failure may start at a stress raiser on the surface of the rod (e.g., which may be due to tensile failures caused by the repeated stresses). The incurred crack may progress in a direction perpendicular to the stress across the sucker rod, therefore reducing the cross-sectional area capable of carrying the load, at which point the rod breaks.
  • Rod failure may be prevented or reduced using stress analysis. Accordingly, what is needed are techniques and apparatus for stress analysis in sucker rod pumping systems.
  • the definition of the fatigue endurance limit for any material, pertaining to steel rods, is the maximum stress level at which the steel can sustain cyclic loading conditions for a minimum of ten million cycles. Additionally, changes in cross-sectional area may create areas of higher local stress. Maintaining rod stress within safe limits may help prevent rod failure.
  • FIG. 2 is a flow chart illustrating example operations 200 for determining stress along a sucker rod string disposed in a wellbore, in accordance with certain aspects of the present disclosure.
  • the operations 200 may be performed by a processor (e.g., control unit 110).
  • the operations 200 may include, at 202, receiving measured (e.g., using one or more sensors) rod displacement and rod load data for the sucker rod string (e.g., rod string 102), wherein the sucker rod string comprises a plurality of sections (e.g., tapers).
  • a plurality of finite difference nodes may be selected such that the selected finite difference nodes have a uniform spacing in at least one of the plurality of sections.
  • the finite difference nodes may be selected such that the uniform spacing satisfies a stability condition.
  • stress values may be calculated at the plurality of finite difference nodes for the at least one of the plurality of sections based, at least in part, on the measured rod displacement and rod load data. As will be discussed in more detail below, the stress values may be calculated using the Modified Everitt-Jennings algorithm for the selected finite difference nodes.
  • the calculated stress values at the plurality of finite difference nodes may be interpolated (e.g., using cubic spline interpolation) to determine stress values (e.g., minimum stress, maximum stress, and/or maximum allowable stress) at one or more points on the at least one section of the sucker rod string (e.g., at any depth).
  • stress values e.g., minimum stress, maximum stress, and/or maximum allowable stress
  • the interpolated stress values may be output to a display (e.g., connected with the control unit 110).
  • a display e.g., connected with the control unit 110.
  • the interpolated stress values for minimum stress, maximum stress, and maximum allowable stress may be displayed (e.g., as shown in FIGs. 12 and 13 ).
  • one or more pump parameters of a rod pump system e.g., stroke speed, stroke length, minimum rod load, or maximum rod load
  • the sucker rod string e.g., reciprocating rod lift system 100
  • one or more pump parameters of a rod pump system e.g., stroke speed, stroke length, minimum rod load, or maximum rod load
  • the sucker rod string e.g., reciprocating rod lift system 100
  • the behavior of the rod string may be simulated (e.g., calculated).
  • One method to control a well is based on fillage calculated from a downhole card. Downhole data can be directly measured by a downhole dynamometer or can be calculated by solving the one-dimensional damped wave equation. However, calculating downhole conditions from measured surface data may be difficult because irreversible energy losses may occur along the rod string due to elasticity.
  • the irreversible energy losses may take the form of stress waves traveling down the rod string at the speed of sound.
  • the one-dimensional damped wave equation may be used to model the propagation of stress waves in an ideal slender bar.
  • downhole conditions may be correctly calculated from the surface data using the one-dimensional damped wave equation.
  • the modified Everitt-Jennings algorithm uses finite differences to solve the wave equation in order to model the behavior of the rod string. As part of the algorithm, an iteration on damping, a fluid load line calculation, and a pump fillage calculation are used in an effort to ensure that the downhole data is as accurate as possible.
  • the damping force may be a complex sum of forces acting in the direction opposing the movement of the sucker-rod string, such as fluid forces and mechanical friction acting on the sucker-rod string, couplings, and tubing. Coulombs or mechanical friction effects may not be considered because of their dependence on unknown factors, such as deviation and corrosion.
  • the fluid forces may be approximated by the viscous forces arising in the annular space. For example, let A represent the sucker-rod string's cross-sectional area (in. 2 ) and k represent the friction coefficient. In order to account for varying rod diameters, Eq.
  • the Modified Everitt-Jennings algorithm may be used to solve the linear hyperbolic differential equation of Eq. 4.
  • the Modified Everitt-Jennings method uses a finite difference model.
  • the Modified Everitt-Jennings algorithm may combine a finite difference engine to solve the wave equation along with a Pump Fillage Calculation (PFC), capable of computing accurate pump fillage regardless of downhole conditions and a Fluid Load Line Calculation (FLLC), which uses calculus and statistics to not only compute fluid load for a stroke, but also to approximate the amount of mechanical friction present in that particular stroke.
  • PFC Pump Fillage Calculation
  • FLLC Fluid Load Line Calculation
  • the Modified Everitt-Jennings may incorporate an iteration on damping, using either single or dual damping factors.
  • First-order-correct forward differences may be used as analogs for the first derivative with respect to time and second-order-correct central differences may be used as analogs for the second derivative with respect to time.
  • a slightly rearranged second-order-correct central difference may used as the analog for the second derivative with respect to position to account for different taper properties.
  • the boundary conditions for Eq. 4 may be obtained directly from the surface position-versus-time and load-versus-time data. Because only the periodic solutions may be desired, initial conditions may not be used in Eq. 4.
  • N represent the number of recorded surface data points and M be the total number of finite difference nodes along the rod string down the wellbore, such that the Mth finite difference node may be the last point above the pump.
  • i 1 M represent the vector of finite difference nodes along the rod string.
  • Let j 1 N represent the vector of sample points taken at the surface.
  • g PR 1 N be the discrete function for the surface polished rod position-versus-time data and let f PR 1 N be the discrete function for the surface polished rod load-versus-time data.
  • the stability condition associated with the above finite difference diagnostic model may be given as shown in Equation 10: ⁇ ⁇ x v ⁇ ⁇ ⁇ t ⁇ 1
  • the stability condition is satisfied when the ratio of the distance between the finite difference nodes-which is a uniform distance-to the product of the acoustic velocity in the rod sting and the sampling time is equal to or less than 1.
  • using finite differences as a tool to solve the wave equation enables the creation of a mesh (e.g., a space and time discretization) at each finite difference node for which position, load and, therefore, stress may be computed.
  • a mesh e.g., a space and time discretization
  • aspects of the present disclosure provide an enhanced stress analysis using the Everitt-Jennings algorithm to calculate stress at any depth along a sucker rod string including uniform selection of the finite difference nodes and polynomial interpolation of stress calculations.
  • a tapered string includes multiple sections (e.g., "tapers"), each section having a different outer diameter, which generally decreases with increasing depth in a wellbore.
  • Each section, or taper may include one or more individual rod elements having that particular diameter.
  • FIG. 14 is a diagram of an example tapered sucker rod string 1400 having a plurality of sections, in accordance with certain aspects of the present disclosure.
  • the tapered sucker rod string 1400 is shown as having four tapers 1402, 1402, 1404, and 1406, this is merely exemplary, and the tapered sucker rod string 1400 could have more or less than four tapers.
  • Tapers in the rod string 1400 may be of different lengths and materials.
  • the weight of the sucker-rod string is distributed along its length, meaning any rod element carries at least the weight of the rod elements below.
  • the rod string may be designed to take into account deviation and corrosion, so that the rod string provides operation without failure for a reasonable amount of time (e.g., ten million cycles).
  • Rod string design may involve determining rod size, lengths of the individual taper section, and the rod material used.
  • Rod strings are subject to cyclic loading, which creates a pulsating tension on the rod string.
  • the rod elements carry the load of the fluids, the dynamic loads, and the friction forces, while on the downstroke the rod elements carry the weight of the rod elements below, this time without the dynamic loads and friction.
  • changes in cross-sectional area in the rod string create areas of concentrated local stress.
  • the maximum tensile and compressive stress to which the rod string may be subjected may be determined.
  • the rod string may be more or less susceptible to failure at different locations of the taper.
  • the rod string Before solving the wave equation for the downhole data, the rod string may be divided into M finite difference nodes.
  • the selection of the spacing for the nodes may be done per taper, as the properties of the tapers may vary.
  • the finite difference elements, or nodes may be selected in such a way that the ⁇ x or spacing in between each node is of similar magnitude for each taper. For example, an initial number of finite difference nodes (per taper) may be selected to satisfy the stability condition.
  • the minimum ⁇ x for all tapers may then be used to compute the number of finite difference elements for the rest of the tapers to ensure a uniform mesh.
  • the use of a quasi-uniform mesh may allow for a more detailed and practical analysis of the stress functions.
  • using finite differences to solve the wave equation may enable for the computation of position, load, and stress at any level down the rod string.
  • techniques for interpolating e.g., cubic spline interpolation
  • the stress data are provided, so that a stress value can be output at any level down the rod string.
  • the stress data may be a series of taper-specific values.
  • the progression of the stress data per-taper may be quasi-linear.
  • the maximum tensile stress may occur at the bottom surface, while the maximum compression stress may occur at the top surface.
  • the stress values may vary linearly from the top surface to the bottom surface. However, stress raisers along the rod may cause the stress values to vary non-linearly.
  • Taylor polynomials when used to interpolate a polynomial function, agree closely with the given function at a specific point, but the best accuracy is only available near that point. It may be desirable for interpolation to provide an accurate approximation over the entire interval.
  • Another approach for interpolating a discrete function may involve piecewise polynomial approximation.
  • the interval is split into several sub-intervals on which a different interpolating polynomial is generated.
  • High-degree polynomials can have an oscillatory nature, which implies that even the slightest fluctuation over a portion of the interval could produce large fluctuations over the entire interval.
  • the simplest piecewise-polynomial interpolation is piecewise linear interpolation.
  • the behavior of the stress data in the event of a stress raiser or a possible failure ceases to be linear. This implies that using piecewise linear interpolation may not be sufficiently accurate and could potentially hide the increased peak that would denote an area of high normal stress concentration.
  • cubic spline interpolation may be used. Cubic spline interpolation may be used to approximate stress at each taper using only four constants for each stress data point.
  • One advantage of using a cubic spline interpolation is that it is relatively simple. Also, because cubic splines are third-degree polynomials, cubic splines are, therefore, continuously differentiable on the taper interval, providing a continuous second derivative. Hence, calculus methods may be used on the smooth cubic spline interpolant in order to search for possible stress raisers and imperfections in the stress data, which could in turn imply a future failure.
  • a cubic spline interpolant may be generated for each taper.
  • the tridiagonal system generated during the cubic spline interpolation may then be solved, for example, using Crout Factorization or similar methods.
  • Downhole data may be computed for a particular stroke.
  • the downhole data may include N position values for each of the M finite difference nodes down the rod string.
  • N load values may be obtained corresponding to the N position values.
  • the computation of maximum allowable stress may use the minimum stress and the taper-specific values of tensile strength and service factor.
  • FIGs. 3 and 4 illustrate an example surface card 300 and an example downhole card 400, respectively, for an example first well, in accordance with certain aspects of the present disclosure.
  • FIG. 5 is a table 500 showing the rod configuration for the first example well, in accordance with certain aspects of the present disclosure.
  • the first example well represents a deep well where steel rod elements (e.g., having a first tensile strength and service factor) combined with sinker bars are used.
  • the stroke represents a full or near full pump fillage card
  • FIGs. 6 and 7 illustrate an example surface card 600 and an example downhole card 700, respectively, for a second example well, in accordance with certain aspects of the present disclosure.
  • FIG. 8 is a table 800 showing the rod configuration for the second example well, in accordance with certain aspects of the present disclosure.
  • the second example well represents a shallower well than the first example well, and grade KD rod elements are used in the second example well, which would suggest a heavy-load application in an effectively inhibited corrosive environment.
  • the KD rod elements are AISI 4720 nickel-chromium-molybdenum alloy steel (e.g., having a second tensile strength and service factor).
  • FIG. 9 is an example table 900 showing results of stress analysis for the second well, in accordance with certain aspects of the present disclosure.
  • the finite difference element distribution (third column in table 900) is displayed as related to the depth (first column in table 900) and taper number (second column in table 900).
  • the matching values for the minimum stress, maximum stress and maximum allowable stress are also displayed in the fourth, fifth, and sixth columns, respectively, in table 900.
  • the total number of finite difference elements M is 50.
  • the total number of finite difference elements M is 80.
  • FIG. 10 is a graph 1000 showing the results of stress analysis for the first example well, in accordance with certain aspects of the present disclosure.
  • FIG. 11 is a graph 1100 showing the results of stress analysis for the second example well from the table 900, in accordance with certain aspects of the present disclosure.
  • the first taper 1002 (or 1102), second taper 1004 (or 1104), third taper 1006 (or 1106), and fourth taper 1008 (or 1108) illustrated in FIG. 10 (or FIG. 11 ), may correspond to the tapers 1402, 1404, 1406, and 1408 illustrated in FIG. 14 .
  • the results of the stress analysis for the minimum stress, the maximum stress, and the maximum allowable stress are plotted against the depth.
  • the marker points on each of the three curves represent the finite difference nodes or elements.
  • the minimum stress starts at 10872 psi/in 2 and decreases to 5204 psi/in 2 for the first taper 1002.
  • the minimum stress starts at 6674 psi/in 2 decreasing to 1590 psi/in 2 .
  • the minimum stress decreases from 2383 psi/in 2 to -2565 psi/in 2 .
  • the minimum stress decreases from 2390 psi/in 2 to -2986 psi/in 2 .
  • the maximum stress for the first example well varies in a similar manner as the minimum stress.
  • the maximum stress starts at 33964 psi/in 2 and decreases to 25599 psi/in 2 for the first taper 1002.
  • the maximum stress decreases from 33351 psi/in 2 to 23572 psi/in 2 .
  • the maximum stress decreases from 32159 psi/in 2 to 22839 psi/in 2 .
  • the maximum stress decreases from 3691 psi/in 2 to 2802 psi/in 2 .
  • the maximum allowable stress for the first example well varies in a similar manner as the minimum and maximum stress, but with increased amplitude.
  • the maximum allowable stress starts at 54061 psi/in 2 and decreases to 51951 psi/in 2 .
  • the maximum allowable stress decreases from 52502 psi/in 2 to 50596 psi/in 2 .
  • the maximum allowable stress decreases from 50893 psi/in 2 to 49037 psi/in 2 .
  • the maximum allowable stress decreases from 21155 psi/in 2 to 20820 psi/in 2 .
  • the minimum stress starts at 9596 psi/in 2 and decreases to 5364 psi/in 2 for the first taper 1102.
  • the minimum stress decreases from 6699 psi/in 2 to 1518 psi/in 2 .
  • the minimum stress decreases from 2059 psi/in 2 to -1753 psi/in 2 .
  • the minimum stress decreases from -1352 psi/in 2 to -2377 psi/in 2 .
  • the maximum stress for the second example well varies in a similar manner as the minimum stress.
  • the maximum stress starts at 24511 psi/in 2 and decreases to 18654 psi/in 2 for the first taper 1102.
  • the maximum stress decreases from 24062 psi/in 2 to 15596 psi/in 2 .
  • the maximum stress decreases from 21032 psi/in 2 to 14379 psi/in 2 .
  • the maximum stress decreases from 1872 psi/in 2 to 693 psi/in 2 .
  • the maximum allowable stress for the second example well varies in a similar manner as the minimum and maximum stress, but with increased amplitude.
  • the maximum allowable stress starts at 25315 psi/in 2 and decreases to 23053 psi/in 2 for the first taper 1102.
  • the maximum allowable stress decreases from 30892 psi/in 2 to 28124 psi/in 2 .
  • the maximum allowable stress decreases from 28413 psi/in 2 to 26589 psi/in 2 .
  • the maximum allowable stress decreases from 26375 psi/in 2 to 26042 psi/in 2 .
  • the calculated peak stress may be close to the maximum allowable stress. This implies that the rod elements in the first taper 1102 are highly loaded, which in turn implies that these rod elements may fail sooner than what is expected when considering the yield strength and tensile strength of these rod elements.
  • minimum stress, maximum stress, and maximum allowable stress may be interpolated using cubic splines or another polynomial interpolation in an effort to produce a smooth function to enable the computation of minimum stress, maximum stress, and maximum allowable stress at any depth down the rod string.
  • piecewise linear interpolation may be used to interpolate stress values at that point.
  • FIGs. 12 and 13 are tables 1200, 1300 showing example interpolated results for the minimum stress, maximum stress, and maximum allowable stress at a given depth for the first example well and the second example well, respectively.
  • the stress results are interpolated for a depth of 1637 ft.
  • this depth occurs in the first taper 1002, in between finite difference element 18 and 19.
  • the interpolated values for minimum stress, maximum stress, and maximum allowable stress are 6016 psi/in 2 , 26949 psi/in 2 , and 52256 psi/in 2 , respectively.
  • this depth occurs in the second taper 1004, in between elements 1 and 2.
  • the interpolated values for minimum stress, maximum stress and maximum allowable stress are 6685 psi/in 2 , 24039 psi/in 2 , and 30885 psi/in 2 , respectively.
  • the ability to compute stress values at any depth down the rod string may allow for improved management of downhole conditions such as deviation or corrosion.
  • the dogleg severity of the wellbore path is above a certain risk angle, it is then possible to focus on the stress values at that point and in the vicinity of that point, providing an improved picture of the loads and stresses for that particular rod section. This may be useful for anticipating rod failures.
  • the techniques described above may rely on the accurate computation of downhole data.
  • it is desirable to handle viscous damping properly.
  • the wave equation assumes a vertical-hole model, often it is applied to wells having non-negligible deviation.
  • the Modified Everitt-Jennings algorithm combines robust iteration on damping along with fluid load line computation capable of estimating the presence of mechanical friction in the well. This may ensure accurate downhole data regardless of downhole conditions.
  • the above stress analysis methodology may allow the user to monitor any section of the rod string. Stress values can be computed at every finite difference element, which can be spaced apart as small as a few feet, for example. Additionally, the capability to compute interpolated stress values at any depth may allow the user in-depth inspection of the stress distribution at a certain point or series of points, completing the stress analysis picture.
  • determining encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, and the like. As used herein, a phrase referring to "at least one of" a list of items refers to any combination of those items, including single members.
  • the methods disclosed herein comprise one or more steps or actions for achieving the described method.
  • the method steps and/or actions may be interchanged with one another without departing from the scope of the claims.
  • the order and/or use of specific steps and/or actions may be modified without departing from the scope of the claims.
  • the computer-readable medium may comprise any suitable memory for storing instructions, such as read-only memory (ROM), random access memory (RAM), flash memory, an electrically erasable programmable ROM (EEPROM), a compact disc ROM (CD-ROM), or a floppy disk.
  • ROM read-only memory
  • RAM random access memory
  • EEPROM electrically erasable programmable ROM
  • CD-ROM compact disc ROM
  • floppy disk any suitable memory for storing instructions, such as compact disc ROM (CD-ROM), or a floppy disk.

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  • Geology (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Engineering & Computer Science (AREA)
  • Mining & Mineral Resources (AREA)
  • Physics & Mathematics (AREA)
  • Environmental & Geological Engineering (AREA)
  • Fluid Mechanics (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Geochemistry & Mineralogy (AREA)
  • Geophysics (AREA)
  • Shafts, Cranks, Connecting Bars, And Related Bearings (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)
  • Investigating Strength Of Materials By Application Of Mechanical Stress (AREA)
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CN106437682A (zh) * 2016-11-01 2017-02-22 中国石油集团东方地球物理勘探有限责任公司 一种预测油井示功图的方法
WO2018026706A1 (en) * 2016-08-04 2018-02-08 Control Microsystems, Inc. Method of determining pump fill and adjusting speed of a rod pumping system
CN109538190A (zh) * 2017-09-22 2019-03-29 中国石油化工股份有限公司 抽油机井杆柱应力预警方法
CN113027387A (zh) * 2021-02-22 2021-06-25 中国石油天然气股份有限公司 一种油井间抽控制系统及方法
CN116976025A (zh) * 2023-07-28 2023-10-31 西南石油大学 一种基于c#平台的api rp 11l有杆抽油系统计算方法

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US11619225B2 (en) 2020-12-08 2023-04-04 International Business Machines Corporation Identifying potential problems in a pumpjack

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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2018026706A1 (en) * 2016-08-04 2018-02-08 Control Microsystems, Inc. Method of determining pump fill and adjusting speed of a rod pumping system
CN106437682A (zh) * 2016-11-01 2017-02-22 中国石油集团东方地球物理勘探有限责任公司 一种预测油井示功图的方法
CN106437682B (zh) * 2016-11-01 2019-10-01 中国石油集团东方地球物理勘探有限责任公司 一种预测油井示功图的方法
CN109538190A (zh) * 2017-09-22 2019-03-29 中国石油化工股份有限公司 抽油机井杆柱应力预警方法
CN113027387A (zh) * 2021-02-22 2021-06-25 中国石油天然气股份有限公司 一种油井间抽控制系统及方法
CN116976025A (zh) * 2023-07-28 2023-10-31 西南石油大学 一种基于c#平台的api rp 11l有杆抽油系统计算方法
CN116976025B (zh) * 2023-07-28 2024-06-07 西南石油大学 一种基于c#平台的api rp 11l有杆抽油系统计算方法

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CA2895793C (en) 2018-06-05
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