US2008240930A1PendingUtilityA1
Method and System for Optimizing Downhole Fluid Production
Est. expiryOct 13, 2025(expired)· nominal 20-yr term from priority
G06F 30/23F04B 47/02F04B 2201/0206G05B 13/041F04B 2205/04F04B 2203/0209F04B 2201/121F04B 47/022F04B 2201/0202F04B 49/065E21B 43/127
36
PatentIndex Score
0
Cited by
0
References
0
Claims
Abstract
A method and system for pumping unit with an elastic rod system is applied to maximize fluid production. The maximum stroke of the pump and the shortest cycle time are calculated based on all static and dynamic properties of downhole and surface components without a limitation to angular speed of the prime mover. Limitations of structural and fatigue strength are incorporated into the optimization calculation to ensure safe operation while maximizing pumped volume and minimizing energy consumption. Calculated optimal prime mover speed is applied to the sucker rod pump by means of beam pumping, long stroke or hydraulic pumping unit by controlling velocity, acceleration and torque of the electric prime mover or by controlling pressure and flow rate in hydraulically actuated sucker rod pumping system.
Claims
exact text as granted — not AI-modified1 - 14 . (canceled)
15 . A method for determining optimal variable angular velocity Ω of a prime mover (motor speed) of a pumping unit (pumpjack) equipped with a sucker rod connected to a downhole pump for pumping fluid from a well, where the said optimal angular velocity varies over a period of a single pumping cycle in such a way that well production is maximized while maintaining specified limits on stresses in the sucker rod and limits on the motor speed, torque, and energy consumption, comprising the steps of:
(i) using a finite number of parameters p for representing the angular velocity Ω[p] of the motor as a function of one of variables selected from the group of variables comprising polished rod position s, crank position α (for beam pumping units only), or of time t, namely respectively Ω[p](s), Ω[p](α) or Ω[p](t), for an entire single pumping cycle; (ii) providing a dynamic model of the entire pumping system, including both the surface equipment (pumpjack with motor and polished rod) and downhole equipment (sucker rod with downhole pump), for calculating motor torque, stresses in the said sucker rod, and well output production rate in response to a given motor angular velocity Ω[p], the said well output production rate V(Ω) defined as the volume Vol(Ω) pumped during one cycle per cycle period T(Ω), i.e. V(Ω)=Vol(Ω)/T(Ω); and, (iii) determining parameters p, by means of a mathematical algorithm for solving nonlinear constrained optimization problems, for which the motor angular velocity Ω[p] maximizes the well production rate V(Ω) while the following constrains are satisfied:
(a) minimum and maximum rod stresses during entire cycle, resulting from the imposed motor speed Ω, do not exceed specified limits;
(b) motor torque required to impose the motor speed Ω does not exceed a specified limit during said cycle;
(c) angular velocity Ω of the motor is identical at a beginning and end of pumping cycle;
(d) angular velocity Ω of the motor does not exceed a specified limit over the course of pumping cycle; and
(e) motor energy consumption per volume of pumped fluid, calculated from the motor torque and angular velocity during the course of pumping cycle, does not exceed a specified limit.
16 . The method of claim 15 , wherein said angular velocity Ω of the motor is represented in the form of a Fourier series, and said variable angular velocity is determined from the optimal set of Fourier coefficients.
17 . The method of claim 15 , further comprising:
(i) representing the angular velocity Ω of the motor in the following form of Fourier series of polished rod position s in order to satisfy the constraint 1.(iii)(c):
Ω
[
p
]
(
s
)
=
β
Ω
_
0
[
1
+
∑
i
=
1
N
(
γ
i
cos
(
2
π
s
/
s
0
)
+
λ
i
sin
(
2
π
s
/
s
0
)
)
]
(
‘
o
’
)
where vector p=[β, γ 1 , . . . , γ N , λ 1 , . . . , λ N ] consists of Fourier coefficients, Ω 0 is a typical operating constant speed for a given pumpjack, and s 0 denotes the polished rod double stroke length
(ii) providing a mathematical model for calculation of displacements, forces and stresses in the sucker rod and the polished rod during a pumping cycle that would result from the polished rod motion imposed by applying a given variable angular velocity Ω of the motor;
(iii) providing a mathematical model for calculation of the motor torque that is required to impose a given variable angular velocity Ω of the motor, the said model utilizing the polished rod force calculated in model 3.(ii) and the gravity and inertial forces acting on all the components of the pumpjack as defined by its geometry and mass distribution;
(iv) providing a mathematical formula for calculation of motor energy consumption based on the motor torque and angular velocity;
(v) providing a mathematical formula for calculating well output production V(Ω) based on the ratio of the downhole pump stroke length to the stroke period T(Ω); and
(vi) providing mathematical algorithm for determining optimal distribution of motor instantaneous angular velocity over the course of each single pumping cycle by finding an optimal set p=[β, γ 1 , . . . , γ N , λ 1 , . . . , λ N ] of Fourier coefficients such that pumping production V(Ω[p]) is maximized while the constrains listed in claim 1 .(iii)(a)-(e) are satisfied; the said algorithm comprising the following steps:
(a) selecting an initial vector p 0 of the Fourier coefficients and vectors Δp i of their increments for each parameter i=1, . . . 2N+1;
(b) using predictive analysis that incorporates mathematical models described in (ii)-(v) above to calculate production V[p], power consumption P[p], motor torque M[p](s), and stress distribution σ[p](x,t) in the sucker rod for the entire cycle in response to the motor angular velocity Ω[p] determined from the equation ‘O’ above at the following points
p=p 0 and p=p 0 +Δp i (i=1, . . . 2N+1)
(c) calculating partial derivatives of functions V[p], M[p](s), σ[p](x,t), Ω[p](s) and P[p] with respect to parameters p i (i=1, . . . 2N+1) using a finite difference method and the incremental values calculated in 3.(vi)(b) above;
(d) using a first order Taylor expansion and the partial derivatives calculated in (c) above to produce linearized functions V[p], M[p](s), σ[p](x,t) Ω[p](s) and T[p] with respect to the small changes δp i of parameters p i ;
(e) linearizing the optimization problem with respect to δp i by using said linear functions from 3.(vi)(d) in the constraints provided in claim 1 .(iii)(a)-(e) as well as in the optimization function V[p];
(f) using a linear programming method to find δp i that is the solution of the linear optimization problem defined in 3.(vi)(e), namely which maximizes the well production while satisfying the linear constraints on motor torque and speed, stresses in the sucker rod and power consumption;
(g) replacing the initial vector p 0 with p 0 +δp and repeat steps 3.(vi)(b)-(f) until 6p becomes smaller than a selected threshold; and
(h) converting function Ω[p](s) to the function of time or crank position.
18 . The method of claim 15 wherein the optimal variable speed of the prime mover is determined such that one of the following performance indicators is minimized: prime mover energy consumption per volume of pumped fluid, maximum motor torque or the stress range in all the sucker rod segments, while the remaining of these indicators are maintained within the prescribed limits, and the pumping production volume achieves the pre-selected target.
19 . A method for determining optimal velocity U of a polished rod connected with a sucker rod to a downhole pump for pumping fluid from a well, where the said optimal velocity varies over a period of a single pumping cycle in such a way that well production is maximized while maintaining specified limits on the polished rod velocity, stresses in the sucker rod and the energy required to induce the said polished rod velocity, comprising the steps of:
(i) using a finite number of parameters p for representing the polished rod velocity U[p] as a function U[p](s) of polished rod position s or a function U[p](t) of time t, for an entire single pumping cycle; (ii) providing a dynamic model of the downhole equipment (sucker rod with downhole pump) for calculating stresses in the said sucker rod and well output production rate in response to a given polished rod velocity U[p], the said well output production rate V(U) defined as the volume Vol(U) pumped during one cycle per cycle period T(U), i.e. V(U)=Vol(Ω)/T(Ω); and, (iii) determining parameters p, by means of a mathematical algorithm for solving nonlinear constrained optimization problems, for which the polished rod velocity U[p] during said pumping cycle maximizes the well production rate V(U) while the following constrains are satisfied:
(a) minimum and maximum rod stresses during said entire single cycle, resulting from the imposed polished rod velocity U do not exceed specified limits;
(b) polished rod velocity U is equal to zero at the polished rod lowest and highest position;
(c) polished rod velocity U does not exceed a specified limit over the course of the entire pumping cycle; and
(d) energy required to induce the said polished rod movement over the period of one pumping cycle per volume of pumped fluid does not exceed a specified limit.
20 . The method of claim 19 , wherein in order to satisfy the constraint 5.(iii)(b) the said polished rod velocity U is represented in the following form of Fourier series of polished rod position s, defined separately for the upstroke sε(0,s 0 /2) and downstroke sε(s 0 /2,s 0 ) part of the movement (s0 is the polished rod double stroke length):
U
[
p
]
(
s
)
=
∑
i
=
1
N
u
i
U
sin
(
2
π
s
/
s
0
)
for
s
∈
(
0
,
s
0
/
2
)
U
[
p
]
(
s
)
=
∑
i
=
1
N
u
i
D
sin
(
2
π
s
/
s
0
)
for
s
∈
(
s
0
/
2
,
s
0
)
and wherein the said optimal variable polished rod velocity over the course of a single pumping cycle is determined from the optimal set of Fourier coefficients
p=[u 1 U , . . . , u N U , u 1 D , . . . , u N D ].
21 . The method of claim 19 wherein the optimal variable polished rod velocity is determined such that the stress range in all the sucker rod segments is minimized, while the pumping production volume and the energy required to induce the said polished rod movement over the period of one pumping cycle T achieve the pre-selected targets.
22 . The method of claim 19 wherein the optimal variable polished rod velocity is determined such that the energy required to produce the said polished rod movement over the period of one pumping cycle per volume of pumped fluid is minimized, while the pumping production volume and the stress range in all the sucker rod segments achieve the pre-selected targets.
23 . The method of claim 19 wherein the polished rod velocity is controlled by a hydraulically actuated pumping system, wherein the new operating parameters are applied to the pumping system by means of controlling pressure and flow rate within an actuation system of the pumping system to control velocity of polished rod as per calculated optimal motion.
24 . The method of claim 19 wherein variable optimal prime mover angular velocity Ω is calculated from optimal polished rod velocity U using geometry of the pumpjack.
25 . The method of claim 15 or claim 19 wherein measurements from an actual pumping system are used to improve system parameters in the mathematical model used in the optimization process, comprising the steps of:
(i) measuring physical conditions of said pumping system during operation, namely said polished rod load and position, motor torque, energy consumption, tubing and casing pressure and well output; (ii) comparing the model of the pumping system results and the physical conditions as measured to verify and adjust the model of the pumping system parameters; (iii) calculating new optimal angular velocity Ω of the motor or new optimal velocity U of a polished rod, based on the model of the pumping system with adjusted system parameters.
26 . The method of claim 15 or claim 24 wherein the prime mover is an electric motor or internal combustion engine, wherein the variable speed is applied to the pumping system by means of controlling instantaneous reducer ratio.
27 . A system for controlling pumping speed in a pumpjack system, comprising:
(i) an electric motor prime mover to control motion of the pumpjack; (ii) a variable frequency drive (VFD) controller for dynamically controlling instantaneous angular velocity of the prime mover within entire pumping cycle; (iii) downhole pumping components including a sucker rod to communicate motion of the pumpjack to a downhole pump; (iv) measuring means for monitoring operational conditions; and (v) a local control unit capable of transmitting instantaneous prime mover speed to a VFD and receiving instantaneous speed and torque of the prime mover from the VFD; a said unit comprising software that incorporates the model of the pumping system and numerical solution techniques for analyzing transmitted information, evaluating performance of the pumping unit and downhole components, and determining optimal prime mover speed according to claim 15 , which are applied to control the prime mover speed at predetermined time steps within the entire pumping cycle.
28 . A system for controlling pumping speed in a pumpjack system, comprising:
(i) an electric motor prime mover to control motion of the pumpjack; (ii) a variable frequency drive (VFD) controller for dynamically controlling instantaneous angular velocity of the prime mover within entire pumping cycle; (iii) downhole pumping components including a sucker rod to communicate motion of the pumpjack to a downhole pump; (iv) measuring means for monitoring operational conditions; and (v) a local control unit capable of transmitting instantaneous prime mover speed to a VFD and receiving instantaneous speed and torque of the prime mover from the VFD; a said unit comprising software that incorporates the model of the pumping system and numerical solution techniques for analyzing transmitted information, evaluating performance of the pumping unit and downhole components, and determining optimal prime mover speed according to claim 24 , which are applied to control the prime mover speed at predetermined time steps within the entire pumping cycle.
29 . A system for controlling pumping speed in a pumpjack system, comprising:
(i) an electric motor prime mover to control motion of the pumpjack; (ii) a variable frequency drive (VFD) controller for dynamically controlling instantaneous angular velocity of the prime mover within an entire pumping cycle; (iii) downhole pumping components including a sucker rod to communicate motion of the pumpjack to a downhole pump; (iv) measuring means for monitoring operational conditions; (v) a local control unit capable of transmitting instantaneous prime mover speed to a VFD and receiving instantaneous speed and torque of the prime mover from the VFD; (vi) signal transmission means for transmitting information in real time from the local control unit to a remote computing station; (vii) said remote computing station equipped with the software that incorporates the model of the pumping system and numerical solution techniques for analyzing transmitted information, evaluating performance of the pumping unit and downhole components, and determining optimal prime mover speed according to claim 15 , which are applied to control the prime mover speed at predetermined time steps within entire pumping cycle; and (viii) means for transmitting optimal prime mover speed and the new operating parameters from remote computing station to the local control unit for controlling the prime mover speed.
30 . A system for controlling pumping speed in a pumpjack system, comprising:
(i) an electric motor prime mover to control motion of the pumpjack; (ii) a variable frequency drive (VFD) controller for dynamically controlling instantaneous angular velocity of the prime mover within an entire pumping cycle; (iii) downhole pumping components including a sucker rod to communicate motion of the pumpjack to a downhole pump; (iv) measuring means for monitoring operational conditions; (v) a local control unit capable of transmitting instantaneous prime mover speed to a VFD and receiving instantaneous speed and torque of the prime mover from the VFD; (vi) signal transmission means for transmitting information in real time from the local control unit to a remote computing station; (vii) said remote computing station equipped with the software that incorporates the model of the pumping system and numerical solution techniques for analyzing transmitted information, evaluating performance of the pumping unit and downhole components, and determining optimal prime mover speed according to claim 24 , which are applied to control the prime mover speed at predetermined time steps within entire pumping cycle; and (viii) means for transmitting optimal prime mover speed and the new operating parameters from remote computing station to the local control unit for controlling the prime mover speed.
31 . The system of claim 27 , claim 28 , claim 29 , or claim 30 wherein the optimal prime mover speed is applied at predetermined polished rod positions.
32 . The system of claim 27 , claim 28 , claim 29 , or claim 30 wherein the optimal prime mover speed is applied at predetermined crank positions.
33 . The system of claim 27 , claim 28 , claim 29 , or claim 30 wherein the measuring means are for measuring polished rod load, polish rod position, tubing and casing pressure.
34 . The system of claim 27 , claim 28 , claim 29 , or claim 30 wherein the VFD comprises one of a dynamic braking resistor and a regenerative module.Join the waitlist — get patent alerts
Track US2008240930A1 — get alerts on status changes and closely related new filings.
We store only your email — no account needed. See our privacy policy.