Detailed Description
As shown in FIG. 2, the method for continuously measuring the working fluid level of the rod-pumped well is characterized in that: which comprises the following steps:
(1) analyzing the dynamic characteristics of the sucker rod, establishing a vibration model of the sucker rod string, and establishing a one-dimensional second-order partial differential equation for describing the motion of the sucker rod string;
(2) iteratively calculating a damping coefficient by using a ground indicator diagram;
(3) obtaining the suspension point load value F at the zero position of the acceleration of the down stroke and the up strokedAnd Fu;
(4) According to FdAnd FuSolving the liquid column load on the full plunger area of the working fluid level depth in the oil well, and further solving the working fluid level H of the oil well;
(5) removing accidental errors and optimizing a calculation result;
(6) and calibrating the working fluid level data of the oil well.
The method and the device provided by the invention can be used for optimizing the result and reducing the measurement error while realizing the real-time calculation of the working fluid level of the oil well, and can be used for calibrating by means of the external working fluid level data under the condition of external data, so that the measurement precision of the working fluid level of the oil well is further improved.
In addition, the one-dimensional second-order partial differential equation in the step (1) is a formula (1-3)
Wherein
Is the damping coefficient of the liquid in the well to the sucker rod, and the unit is s
-1;
The propagation speed of the stress wave in the sucker rod is expressed in m/s.
In addition, the mathematical model for simulating the vibration of the sucker rod in the step (1) comprises the following steps: wave equation, boundary conditions, initial conditions, and continuity conditions.
In addition, the specific calculation formula of the damping coefficient in the step (2) is formula (1-16):
wherein
The stroke length of the polish rod is divided by the area integral of the upper stroke and the lower stroke of the polish rod indicator diagram respectively;
the pumping unit is obtained by dividing the area integral of the upper stroke and the lower stroke of a pump diagram by the pump stroke, wherein alpha is the structural coefficient of the pumping unit, and T is the period;
the convergence condition of equations (1-16) is:
wherein ε is the allowable error;
in addition, the step (3) comprises the following substeps:
(3.1) averaging the abscissa of any discrete point of the pump diagram by using a five-point averaging method
(3.2) by displacing the maximum and minimum values of the abscissa of the discrete point on the data:
Xmax,Xmin;
(3.3) carrying out normalization processing on the displacement of the pump work diagram;
(3.4) calculating the curvature value k of each discrete point on the pump diagram according to the formula (1-20)i
(3.5) averaging the curvatures by the five-point method
(3.6) k 'in the vertical stroke was obtained'iValue of i at 0, if k'i>0,k′i+1< 0 or k'i+1>0,k′i<0
In addition, the step (4) comprises the following substeps:
(4.1) solving the liquid column load W on the full plunger area of the working fluid level depth in the oil wellL
WL=Fu-Fd-(Pt-Pc)×Ap (1—21)
Wherein P istThe well head back pressure is Pa; pcIs sleeve pressure, Pa; a. thepIs the area of the plunger, m2;
(4.3) solving the working fluid level H
In addition, the step (5) comprises the following substeps:
(5.1) solving the average value of the calculated working fluid level H of the last five times
(5.4) eliminating points with the relative error between the calculation result and the average value being more than 20 percent
(5.5) averaging the residual values to obtain the current working fluid level data H, if the relative errors of all the data are more than 20%, the calculation is failed, the current production condition of the oil well is unstable, and the calculation is carried out after 5 complete strokes are waited;
dynamic liquid level H for time point of failure of calculationiPerforming supplementary calculation according to the formulas (1-25),
in addition, the calibration of the working fluid level calculation in the step (6) adopts the combination of actually measured working fluid level data h of the oil welliCarry out calibration
Hbi=μHi (1—26)
As shown in fig. 1, there is also provided a continuous measuring device for the working fluid level of a rod-pumped well, comprising: the device comprises a diagram acquisition unit, a pressure acquisition unit and a data processing unit; the indicator diagram acquisition unit comprises a load sensor and an angular displacement sensor; the pressure acquisition unit comprises a back pressure measurement sensor and a sleeve pressure measurement sensor.
The method comprises the steps of firstly, acquiring current load and angular displacement data of each stroke of an oil well and corresponding back pressure and casing pressure through a sensor. And forming a polished rod indicator diagram of the oil well by using the load data and the displacement data.
The present invention is described in detail below.
The embodiment of the invention provides a continuous measurement and calculation process of the working fluid level of an oil pumping well, which comprises the following steps:
【1】 Analyzing the dynamic characteristics of the sucker rod, establishing a vibration model of the sucker rod string, establishing a one-dimensional second-order partial differential equation, namely a wave equation, describing the motion of the sucker rod string, further solving the wave equation,
in the formula
Damping coefficient of well liquid to sucker rod, s
-1;
The propagation speed of the stress wave in the sucker rod is m/s.
The sucker rod simulation vibration mathematical model comprises the following four aspects: wave equation, boundary conditions, initial conditions, and continuity conditions.
(1) Boundary condition
The boundary condition is determined according to the law of the motion of the suspension point of the pumping unit and can be solved according to the geometric motion characteristic of the pumping unit.
u(x,t)|x=0=u(t) (1-4)
(2) Initial conditions
Setting an initial moment, enabling the oil well pump piston to be located at a bottom dead center to prepare for moving upwards from the bottom dead center, and actually measuring the load and the displacement on the ground indicator diagram as initial conditions.
Wherein u (t) is the displacement of the actually measured ground indicator diagram; d (t) is the load of the actually measured ground indicator diagram; wrThe weight of the sucker rod string in the well fluid.
(3) Conditions of continuity
For multi-stage sucker rods with different diameters and different materials, the load and displacement continuity conditions of the junction of the two stages of rods and columns are as follows:
the mathematical model of the vibration simulation of the sucker rod string is obtained by the formulas (1-3), (1-4), (1-5) and (1-6):
judging whether the sucker rod is the last sucker rod or not, if so, calculating to obtain a displacement load relationship which is a pump diagram, and finishing the calculation; otherwise, calculating the second-stage rod column end u according to the force continuity principle2(xiT) and F2(xiAnd t) calculating sequentially until the tail end of the last lever, and obtaining the corresponding pump indicator diagram.
Solving a mathematical model wave equation of the vibration of the sucker rod string by adopting a Fourier series method:
and (3) respectively expanding D (t) and u (t) into Fourier series by taking a suspension point dynamic load function as D (t) and a polished rod displacement function u (t) as boundary conditions:
wherein N represents the number of Fourier series terms; sigmao,γo,σn,τn,vn,δn(N-1, 2, …, N) represents a fourier coefficient, and w represents a crank angular velocity.
The Fourier coefficient of the change of the dynamic load and the displacement of the sucker rod is obtained by the numerical integration of the actually measured D (t) curve and u (t) curve:
where N is 0,1,2,.., N, d (p) and u (p) are the load and displacement, respectively, of discrete points of the indicator diagram.
And (1-7) is taken as a boundary condition, the equation (1-8) is solved by using a separation variable method, and the change of the displacement of the sucker rod string at any depth along with the time can be obtained:
from hooke's law one can derive:
the variation of the dynamic load with time can be obtained according to the equation (1-12) as follows:
at time t, the total load F (x, t) on section x is the weight of the rod string below section x plus.
In the formulae (1-12) (1-13):
wherein alpha isn,βn,kn,μn,an,bn,cn,dnAre all special constants:
【2】 Through trial calculation, a method for iteratively calculating the damping coefficient by using a ground indicator diagram is selected.
The specific calculation formula of the damping coefficient is as follows:
in the formula (I), the compound is shown in the specification,
the stroke length of the polish rod can be obtained by dividing the integral of the areas of the upper stroke and the lower stroke of the polish rod indicator diagram by the stroke length of the polish rod;
the pumping unit is obtained by dividing the area integral of the up stroke and the down stroke of a pump diagram by the pump stroke respectively, wherein alpha is the structural coefficient of the pumping unit, and T is the period.
When the damping coefficient is solved by using the formula (1-16), the pump indicator diagram must be known first, but if the pump indicator diagram is known, the damping coefficient must be known first, so the damping coefficient is solved by adopting an iteration method after setting an initial value.
The convergence condition of the equations (1-16) is:
in which epsilon isTo allow for errors;
【3】 And solving a suspension point load value at the acceleration of zero.
(1) Solving the abscissa average value of any discrete point of the pump diagram by using a five-point averaging method;
(2) by shifting the maximum and minimum of the abscissa of the discrete points on the data: xmax,Xmin;
(3) Carrying out normalization processing on the displacement of the pump work diagram;
(4) calculating the curvature value k of each discrete point on the pump diagram according to the formula (1-20)i;
(5) Averaging curvature by five-point method
To improve the accuracy of the algorithm.
(6) Respectively obtaining k 'in the up-down stroke'iValue of i at 0, if k'i>0,k′i+1< 0 or
k′i+1>0,k′i<0
【4】 And solving the dynamic liquid level H of the oil well.
(1) Solving the liquid column load W on the full plunger area of the working fluid level depth in the oil wellL
WL=Fu-Fd-(Pt-Pc)×Ap (1—21)
Wherein P istThe well head back pressure is Pa; pcIs sleeve pressure, Pa; a. thepIs the area of the plunger, m2;
(2) And solving the working fluid level H.
【5】 And eliminating accidental errors and optimizing a calculation result.
(1) Solving the average value of the calculated working fluid level H of the last five times
(2) And removing points with the relative error of the calculation result and the average value being more than 20%.
(3) And averaging the residual values to obtain the current working fluid level data H, wherein if the relative errors of all the data are more than 20%, the calculation is failed, the current production condition of the oil well is unstable, and the calculation is carried out after 5 complete strokes are waited.
Dynamic liquid level H for time point of failure of calculationiPerforming supplementary calculation according to the formulas (1-25),
【6】 Calibrating the working fluid level data of the oil well;
the calibration of the working fluid level calculation combines the actual measurement of the working fluid level data h of the oil welliAnd (6) calibrating.
Hbi=μHi (1—26)
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the present invention in any way. It should be understood by those skilled in the art that any simple modification, equivalent change and modification made to the above embodiments according to the technical spirit of the present invention still fall within the protection scope of the technical solution of the present invention.