CN103924959B - Method for measuring water content in oil well production fluid - Google Patents

Abstract

The invention discloses a method for measuring water content in oil well produced liquid, which comprises the steps of adopting a sucker rod pump oil extraction system, installing a load sensor, a displacement sensor and an electrical parameter sensor on a wellhead oil pumping unit, obtaining an oil well indicator diagram every 5-15 minutes, calculating an oil well pump indicator diagram from the indicator diagram, obtaining the area of the pump indicator diagram, and obtaining the water content in the produced liquid according to the fact that the area of the pump indicator diagram is equal to the work of lifting the produced liquid in a pump cylinder to the ground. According to the invention, the oil well pump indicator diagram can be rapidly calculated by acquiring the oil well indicator diagram in real time, so that the water content in the oil well output liquid can be calculated, the labor intensity of operators is greatly reduced, and the oil yield of the oil well can be accurately obtained.

Description

Measure the method for water content in oil well liquid-producing

Technical field

The present invention relates to oil extraction in oil field technical field, measure the method for water content in oil well liquid-producing particularly to a kind of.

Background technology

Along with the mankind are increasing to the demand of oil, the development of oil recovery technique is the quickest.The most in the world All petroleum wells in, in produced liquid in oil well, the content of water all occupies certain ratio.In order to accurately grasp every mouthful of oil The oil production of well, then must measure the content of water in oil well liquid-producing, due in oil reservoir production fluid aqueous number be change.Mesh Before, the scene of oil recovery must measure the water content in produced liquid in oil well continually, often within 10 days, is accomplished by measuring once.Tradition oils Field is just can be obtained by a series of programs such as wellhead sampling, laboratory distillation, centrifugal, electric dehydration chemical examinations the determination of well water ?.

During realizing the present invention, inventor finds that prior art at least there is problems in that due to oil well quantity Huge, and existing measurement means needs to spend oil field employee substantial amounts of time, energy and financial resources, substantially increases employee's labor Fatigue resistance, and measure aqueous ageing the strongest, it is impossible to extremely accurate learn well oil output.

Summary of the invention

In order to solve problem of the prior art, embodiments provide and a kind of measure the side of water content in oil well liquid-producing Method.Described technical scheme is as follows:

Provide and a kind of measure the method for water content in oil well liquid-producing, use sucker rod pumping system, at pumping unit of well mouth On install load transducer, displacement transducer and electrical quantity sensor, every 5～15 minutes obtain an oil well indicator card, Calculated oil well pump dynagraoph by described indicator card, and ask for the area of described pump dynagraoph, be equal to according to the area of described pump dynagraoph In pump barrel, production fluid gives rise to ground work done, tries to achieve water content in production fluid.

Further, said method comprising the steps of:

S1, sets up the fault diagnosis model of sucker rod pumping system；

S2, determines passing of rod string each cross section indicator card of sucker rod pump according to the described fault diagnosis model of foundation in S1 Push away form；

S3, is calculated the pump dynagraoph of sucker rod pump according to the described recurrence algorithm determined in S2, and described pump dynagraoph includes position Move function and axle force function；

S4, asks for effective stroke and the pump dynagraoph area of sucker rod pump；

S5, calculates sucker rod pump pump liquid within the cartridge and gives rise to ground work done；

S6, asks for water content in production fluid.

Further, the concrete grammar setting up described fault diagnosis model in step S1 is:

Whole rod string discretization, being set as M unit, the mass concentration of each unit sucker rod string is to unit one On the node of end, form lumped mass m_i, set the tension and compression between each unit and be equivalent to tension and compression rigidity as k_iSpring:

Then, m_i=q_riL_i(1),

In formula (1), q_riBeing the bar weight of the unit length of i-th unit, unit is kg/m；L_iIt is the length of i-th unit, Unit is m；

Described fault diagnosis model is:

$k_i=\frac{E_i{A}_i}{L_i}---\left(2\right),$

In formula (2), E_iBeing the elastic modelling quantity of i-th unit material, unit is Pa；A_iIt it is the cross section face of i-th unit Long-pending, unit is m²。

Further, step S2 determining, described recurrence algorithm is:

Known by Hooke's law: F_i-1=k_i(s_i-s_i-1) (3),

Derive:

Known by cattle top second law again:

Formula (4) is substituted into formula (5), and arranges:

$F_i=m_i{\stackrel{\·\·}{s}}_{i-1}+\frac{m_i}{k_i}{\stackrel{\·\·}{F}}_{i-1}+F_{i-1}-m_{i}g---\left(6\right),$

Formula (4) and formula (6) are denoted as:

$\left\{\begin{array}{c}{s}_i\\ F_i\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ m_i\frac{d^2}{{\mathrm{dt}}^2}& \frac{m_i}{k_i}\frac{d^2}{{\mathrm{dt}}^2}+1\end{array}\right]\left\{\begin{array}{c}{s}_{i-1}\\ F_{i-1}\end{array}\right\}+\left\{\begin{array}{c}0\\ -m_{i}g\end{array}\right\}---\left(7\right),$

Formula (7) is the recurrence algorithm of rod string each cross section indicator card.

Further, in step S3, the computational methods of pump dynagraoph are:

S in setting formula (7)_i-1=s_i-1(θ)、F_i-1=F_i-1(θ)、s_i=s_i(θ) and F_i=F_i(θ) it is all sucker rod pump The function of crank angle θ, expands into Fourier progression them,

$\begin{array}{c}{s}_{i-1}=s_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ})\end{array}---\left(8\right),$

$\begin{array}{c}{F}_{i-1}=F_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ})\end{array}---\left(9\right),$

$\begin{array}{c}{s}_i=s_i\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ})\end{array}---\left(10\right),$

$\begin{array}{c}{F}_i=F_i\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ})\end{array}---\left(11\right),$

Wushu (8), formula (9), formula (10) and formula (11) substitute in formula (7), and set crank uniform rotation,

N is jig frequency, min^-1；Arrangement can obtain:

$\left\{\begin{array}{c}{a}_{i0}\\ d_{i0}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,0}\\ d_{i-1,0}\end{array}\right\}+\left\{\begin{array}{c}0\\ -2m_{i}g\end{array}\right\}---\left(12\right),$

$\left\{\begin{array}{c}{a}_{ij}\\ d_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,j}\\ d_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(13\right),$

$\left\{\begin{array}{c}{b}_{ij}\\ e_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{b}_{i-1,j}\\ e_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(14\right),$

Order:

$\[C_{ij}\]==\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]---\left(15\right),$

Have:

$\left\{\begin{array}{c}{a}_{M0}=a_{00}+\left(\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\right)d_{00}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ d_{M0}=d_{00}-\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right.---\left(16\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(17\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(18\right),$

Above-mentioned formula (16), (17) and (18) is abbreviated as respectively:

$\left\{\begin{array}{c}{a}_{M0}\\ d_{M0}\end{array}\right\}=\left[\begin{array}{cc}1& \underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{00}\\ d_{00}\end{array}\right\}+\left\{\begin{array}{c}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ -\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right\}---\left(19\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(20\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(21\right),$

For described diagnostic cast, the displacement function s of suspension point position₀=s₀(θ)=-s_PR(θ) by the motion of oil pumper Analysis and solution, axle force function F₀=F₀(θ)=F_PR(θ) obtained by interpolation according to displacement function and actual measurement polished rod indicator card；

Displacement function and axle force function are expanded into Fourier progression, it is thus achieved that coefficientWithThen the coefficient at pump is obtained by formula (19), (20) and (21)With

Obtaining the displacement function at pump by the calculating of Fourier level numerical expression (8), (9), (10) and (11) is: s_pump(θ) =-s_M(θ)=-s_M；Axle force function is: F_pump(θ)=F_M(θ)=F_M, i.e. the pump dynagraoph of sucker rod pump.

Further, the acquiring method of effective stroke described in step S4 is by polygonous approximation and vector characteristic method Identify.

Further, pump dynagraoph area described in step S4 is:

$S={\∫}_{x_{min}}^{x_{max}}(F_u-F_d)dx---\left(22\right),$

In formula (22), F_u、F_dBe in a stroke cycle pumping unit horsehead through same position pull bar and pump junction Load, x_min、x_maxIt is pull bar and the least displacement of pump junction point and maximum displacement.

Further, in step S5, sucker rod pump pump liquid within the cartridge gives rise to ground work done and is:

In formula (23), ρ_LiquidBeing oil well liquid-producing density, d is pump barrel internal diameter, and h is dynamic oil level, s_eIt it is pump effective stroke.

Further, in step S6, in production fluid, the acquiring method of water content is:

By: S=W (24),

ρ_Liquid=ρ_WaterV_Water+ρ_Oil(1-V_Water) (25),

Can obtain:

Water content in formula (26) i.e. oil well liquid-producing.

The technical scheme that the embodiment of the present invention provides has the benefit that

By obtaining oil well indicator card in real time such that it is able to calculate oil well pump dynagraoph rapidly, and then calculate oil well Water content in production fluid so that the labor intensity of operator is substantially reduced and can accurately obtain the oil-producing of oil well Amount.

Accompanying drawing explanation

For the technical scheme being illustrated more clearly that in the embodiment of the present invention, in embodiment being described below required for make Accompanying drawing be briefly described, it should be apparent that, below describe in accompanying drawing be only some embodiments of the present invention, for From the point of view of those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to obtain other according to these accompanying drawings Accompanying drawing.

Fig. 1 is the oil pumper sensor installation diagram that the embodiment of the present invention provides；

Fig. 2 is the fault diagnosis simplified model figure that the embodiment of the present invention provides；

Fig. 3 is the pump effective stroke identification process figure that the embodiment of the present invention provides；

Fig. 4 is the cursor indicator card collected of embodiment of the present invention offer and the most calculated pump dynagraoph.

Detailed description of the invention

For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing to embodiment party of the present invention Formula is described in further detail.

Present embodiments providing and a kind of measure the method for water content in oil well liquid-producing, the method is applicable to sucker rod pumping system System, with reference to Fig. 1, first, installs load transducer 1, displacement transducer 2 and electrical quantity sensor 3, often on pumping unit of well mouth Obtained an oil well indicator card every 5～15 minutes, described indicator card calculate oil well pump dynagraoph, and ask for described pump dynagraoph Area, gives rise to ground work done according to the area of described pump dynagraoph equal to production fluid in pump barrel, tries to achieve water content in production fluid.

The method includes step in detail below:

S1, sets up the fault diagnosis model of sucker rod pumping system.The concrete grammar setting up fault diagnosis model is:

With reference to Fig. 2, in the fault diagnosis simplified model of sucker rod pumping system, if the displacement s of rod string is downwards Just, it is upwards negative；Axle power F of rod string draw into just, pressure be negative.Whole rod string discretization, it is set as M unit, Each unit is done following equivalent process: remove the bending stiffness of unit, by the knot of the mass concentration of unit to unit one end On point, wherein, the lateral pressure between the R a T everywhere of the well bore caused by bending stiffness can individually consider.So, The mass concentration of each unit sucker rod string, on the node of unit one end, forms lumped mass m_i, between each lumped mass It is k by tension and compression rigidity_iSpring replace, due to the viscosity of well liquid, between sucker rod and fluid column, there is viscous damping force, its shadow Ringing equivalence becomes damped coefficient to be c_iAntivibrator, additionally, due to the existence of lateral pressure between R a T, sucker rod is also subject to To the effect of non-viscous frictional force, if the coefficient of friction between R a T is μ_i, this just has unlimited certainly one Multi-freedom-degree vibration is turned to by the continuous elastomeric vibration spent.Consider the viscous damping force that is subject to of rod string and non-viscous friction Power can make simplified model become the most complicated, in view of they are inconspicuous on the impact of pump effective stroke, in order to simplify calculating, and pushing away below Them are not considered further that in leading.

I.e. set the tension and compression between each unit and be equivalent to tension and compression rigidity as k_iSpring, owing to not considering in ideal model The quality of spring, so the active force at its two ends is identical, such as: spring k_iThe active force at two ends is all F_i-1；And lumped mass can be recognized For being a particle, so the displacement at its two ends is identifiable, i.e. lumped mass m_iThe displacement at two ends is all s_i, then Have:

m_i=q_riL_i(1),

In formula (1), q_riBeing the bar weight of the unit length of i-th unit, unit is kg/m；L_iIt is the length of i-th unit, Unit is m；

Described fault diagnosis model is:

$k_i=\frac{E_i{A}_i}{L_i}---\left(2\right),$

In formula (2), E_iBeing the elastic modelling quantity of i-th unit material, unit is Pa；A_iIt it is the cross section face of i-th unit Long-pending, unit is m².Wherein, the q of each unit_ri、L_i、E_i、A_iCan be different, so this model is applicable to multistage different materials and takes out The situation of beam hanger post.

S2, determines rod string each cross section indicator card of sucker rod pump according to the described fault diagnosis model set up in step S1 Recurrence algorithm.

Specifically, it is determined that the recurrence algorithm of the rod string of sucker rod pump each cross section indicator card is as follows:

Known by Hooke's law: F_i-1=k_i(s_i-s_i-1) (3),

Derive:

Known by cattle top second law again:

Formula (4) is substituted into formula (5), and arranges:

$F_i=m_i{\stackrel{\·\·}{s}}_{i-1}+\frac{m_i}{k_i}{\stackrel{\·\·}{F}}_{i-1}+F_{i-1}-m_{i}g---\left(6\right),$

Formula (4) and formula (6) are denoted as:

$\left\{\begin{array}{c}{s}_i\\ F_i\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ m_i\frac{d^2}{{\mathrm{dt}}^2}& \frac{m_i}{k_i}\frac{d^2}{{\mathrm{dt}}^2}+1\end{array}\right]\left\{\begin{array}{c}{s}_{i-1}\\ F_{i-1}\end{array}\right\}+\left\{\begin{array}{c}0\\ -m_{i}g\end{array}\right\}---\left(7\right),$

Formula (7) is the recurrence algorithm of rod string each cross section indicator card.

S3, is calculated the pump dynagraoph of sucker rod pump according to the recurrence algorithm determined in step S2, and pump dynagraoph includes displacement letter Number and axle force function.

Shifting function set forth below and the derivation step of axle force function:

S in the recurrence algorithm formula (7) that setting procedure S2 obtains_i-1=s_i-1(θ)、F_i-1=F_i-1(θ)、s_i=s_i(θ) and F_i =F_i(θ) it is all the function of crank angle θ of sucker rod pump, they is expanded into Fourier progression,

$\begin{array}{c}{s}_{i-1}=s_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ})\end{array}---\left(8\right),$

$\begin{array}{c}{F}_{i-1}=F_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ})\end{array}---\left(9\right),$

$\begin{array}{c}{s}_i=s_i\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ})\end{array}---\left(10\right),$

$\begin{array}{c}{F}_i=F_i\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ})\\ \≈\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ})\end{array}---\left(11\right),$

Wushu (8), formula (9), formula (10) and formula (11) substitute in formula (7), and set crank uniform rotation,

N is jig frequency, min^-1；Arrangement can obtain:

$\left\{\begin{array}{c}{a}_{i0}\\ d_{i0}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,0}\\ d_{i-1,0}\end{array}\right\}+\left\{\begin{array}{c}0\\ -2m_{i}g\end{array}\right\}---\left(12\right),$

$\left\{\begin{array}{c}{a}_{ij}\\ d_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,j}\\ d_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(13\right),$

$\left\{\begin{array}{c}{b}_{ij}\\ e_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{b}_{i-1,j}\\ e_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(14\right),$

Order:

$\[C_{ij}\]==\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]---\left(15\right),$

Have:

$\left\{\begin{array}{c}{a}_{M0}=a_{00}+\left(\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\right)d_{00}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ d_{M0}=d_{00}-\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right.---\left(16\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(17\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(18\right),$

Above-mentioned formula (16), (17) and (18) is abbreviated as respectively:

$\left\{\begin{array}{c}{a}_{M0}\\ d_{M0}\end{array}\right\}=\left[\begin{array}{cc}1& \underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{00}\\ d_{00}\end{array}\right\}+\left\{\begin{array}{c}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ -\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right\}---\left(19\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(20\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(21\right),$

For described diagnostic cast, the displacement function s of suspension point position₀=s₀(θ)=-s_PR(θ) by the motion of oil pumper Analysis and solution, axle force function F₀=F₀(θ)=F_PR(θ) obtained by interpolation according to displacement function and actual measurement polished rod indicator card；

Displacement function and axle force function are expanded into Fourier progression, it is thus achieved that coefficientWithThen the coefficient at pump is obtained by formula (19), (20) and (21)With

Obtaining the displacement function at pump by the calculating of Fourier level numerical expression (8), (9), (10) and (11) is: s_pump(θ) =-s_M(θ)=-s_M；Axle force function is: F_pump(θ)=F_M(θ)=F_M, i.e. the pump dynagraoph of sucker rod pump.

S4, asks for effective stroke and the pump dynagraoph area of sucker rod pump.

With reference to Fig. 3, the acquiring method of effective stroke is by polygonous approximation and vector characteristic method identification.

With reference to Fig. 4, pump dynagraoph area is:

$S={\∫}_{x_{min}}^{x_{max}}(F_u-F_d)dx---\left(22\right),$

In formula (22), F_u、F_dBe in a stroke cycle pumping unit horsehead through same position pull bar and pump junction Load, x_min、x_maxIt is pull bar and the least displacement of pump junction point and maximum displacement.

S5, calculates sucker rod pump pump liquid within the cartridge and gives rise to ground work done.

Sucker rod pump pump liquid within the cartridge gives rise to ground work done:

In formula (23), ρ_LiquidBeing oil well liquid-producing density, d is pump barrel internal diameter, and h is dynamic oil level, s_eIt it is pump effective stroke.Its In, pump effective stroke is produced system by existing performance analysis and merit figure meter and obtains.

S6, asks for water content in production fluid.

In production fluid, the acquiring method of water content is:

By: S=W (24),

ρ_Liquid=ρ_WaterV_Water+ρ_Oil(1-V_Water) (25),

Can obtain:

Water content in formula (26) i.e. oil well liquid-producing, ρ_WaterAnd ρ_OilThe density of water and oily density in oil well liquid-producing.

The foregoing is only presently preferred embodiments of the present invention, not in order to limit the present invention, all spirit in the present invention and Within principle, any modification, equivalent substitution and improvement etc. made, should be included within the scope of the present invention.

Claims (7)

1. measure a method for water content in oil well liquid-producing, use sucker rod pumping system, it is characterised in that pump at well head Install load transducer (1), displacement transducer (2) and electrical quantity sensor (3) on machine, obtain one every 5～15 minutes Oil well indicator card, is calculated oil well pump dynagraoph by described indicator card, and asks for the area of described pump dynagraoph, according to described pump dynagraoph Area give rise to ground work done equal to production fluid in pump barrel, try to achieve water content in production fluid, in described measurement oil well liquid-producing The method of water content comprises the following steps:

S1, sets up the fault diagnosis model of sucker rod pumping system；

S2, determines the recursion lattice of rod string each cross section indicator card of sucker rod pump according to the described fault diagnosis model set up in S1 Formula；

S3, is calculated the pump dynagraoph of sucker rod pump according to the described recurrence algorithm determined in S2, and described pump dynagraoph includes displacement letter Number and axle force function；

S4, asks for effective stroke and the pump dynagraoph area of sucker rod pump；

S5, calculates sucker rod pump pump liquid within the cartridge and gives rise to ground work done；

S6, gives rise to ground work done according to the area of described pump dynagraoph equal to production fluid in pump barrel, tries to achieve in production fluid aqueous Amount；

The concrete grammar setting up described fault diagnosis model in step S1 is:

Whole rod string discretization, being set as M unit, the mass concentration of each unit sucker rod string is to unit one end On node, form lumped mass m_i, set the tension and compression between each unit and be equivalent to tension and compression rigidity as k_iSpring:

Then, m_i=q_riL_i(1),

In formula (1), q_riBeing the bar weight of the unit length of i-th unit, unit is kg/m；L_iIt is the length of i-th unit, unit It is m；

Described fault diagnosis model is:

$k_i=\frac{E_i{A}_i}{L_i}---\left(2\right),$

In formula (2), E_iBeing the elastic modelling quantity of i-th unit material, unit is Pa；A_iIt is the cross-sectional area of i-th unit, single Position is m²。

The method of water content in measurement oil well liquid-producing the most according to claim 1, it is characterised in that determine institute in step S2 Stating recurrence algorithm is:

Known by Hooke's law: F_i-1=k_i(s_i-s_i-1) (3),

F_i-1It is the axle power of the i-th-1 unit, s_iFor the displacement of described i-th unit, s_i-1Displacement for described the i-th-1 unit；

Derive:

Known by Newton's second law again:

F_iFor the axle power of described i-th unit,For s_iSecond dervative；

Formula (4) is substituted into formula (5), and arranges:

$F_i=m_i{\stackrel{\·\·}{s}}_{i-1}+\frac{m_i}{k_i}{\stackrel{\·\·}{F}}_{i-1}+F_{i-1}-m_{i}g---\left(6\right),$

For F_i-1Second dervative,For s_i-1Second dervative；

Formula (4) and formula (6) are denoted as:

$\left\{\begin{array}{c}{s}_i\\ F_i\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ m_i\frac{d^2}{{\mathrm{dt}}^2}& \frac{m_i}{k_i}\frac{d^2}{{\mathrm{dt}}^2}+1\end{array}\right]\left\{\begin{array}{c}{s}_{i-1}\\ F_{i-1}\end{array}\right\}+\left\{\begin{array}{c}0\\ -m_{i}g\end{array}\right\}---\left(7\right),$

Representing and time t is asked for second dervative, formula (7) is the recurrence algorithm of rod string each cross section indicator card.

The method of water content in measurement oil well liquid-producing the most according to claim 2, it is characterised in that pump dynagraoph in step S3 Computational methods be:

S in setting formula (7)_i-1=s_i-1(θ)、F_i-1=F_i-1(θ)、s_i=s_i(θ) and F_i=F_i(θ) it is all that the crank of sucker rod pump turns The function of angle θ, expands into Fourier progression them,

$\begin{array}{c}{s}_{i-1}=s_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}\left(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ}\right)\\ \≈\frac{1}{2}{a}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\left(a_{i-1,j}\cos j\mathrm{\θ}+b_{i-1,j}\sin j\mathrm{\θ}\right)\end{array}---\left(8\right),$

$\begin{array}{c}{F}_{i-1}=F_{i-1}\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}\left(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ}\right)\\ \≈\frac{1}{2}{d}_{i-1,0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\left(d_{i-1,j}\cos j\mathrm{\θ}+e_{i-1,j}\sin j\mathrm{\θ}\right)\end{array}---\left(9\right),$

$\begin{array}{c}{s}_i=s_i\left(\mathrm{\θ}\right)=\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}\left(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ}\right)\\ \≈\frac{1}{2}{a}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\left(a_{ij}\cos j\mathrm{\θ}+b_{ij}\sin j\mathrm{\θ}\right)\end{array}---\left(10\right),$

$\begin{array}{c}{F}_i=F_i\left(\mathrm{\θ}\right)=\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{\mathrm{\∞}}{\mathrm{\Σ}}}\left(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ}\right)\\ \≈\frac{1}{2}{d}_{i0}+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\left(d_{ij}\cos j\mathrm{\θ}+e_{ij}\sin j\mathrm{\θ}\right)\end{array}---\left(11\right),$

Wushu (8), formula (9), formula (10) and formula (11) substitute in formula (7), and set crank uniform rotation,N is punching Secondary, min^-1； For the first derivative of described crank angle θ,For the second dervative of described crank angle θ, ω is crank Angular velocity, arrangement can obtain:

$\left\{\begin{array}{c}{a}_{i0}\\ d_{i0}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,0}\\ d_{i-1,0}\end{array}\right\}+\left\{\begin{array}{c}0\\ -2m_{i}g\end{array}\right\}---\left(12\right),$

$\left\{\begin{array}{c}{a}_{ij}\\ d_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{a}_{i-1,j}\\ d_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(13\right),$

$\left\{\begin{array}{c}{b}_{ij}\\ e_{ij}\end{array}\right\}=\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]\left\{\begin{array}{c}{b}_{i-1,j}\\ e_{i-1,j}\end{array}\right\},j=1,2,...,N---\left(14\right),$

Order:

$\[C_{ij}\]==\left[\begin{array}{cc}1& \frac{1}{k_i}\\ -j^2{\mathrm{\ω}}^2{m}_i& -j^2{\mathrm{\ω}}^2\frac{m_i}{k_i}+1\end{array}\right]---\left(15\right),$

Have:

$\left\{\begin{array}{c}{a}_{M0}=a_{00}+\left(\underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\right)d_{00}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ d_{M0}=d_{00}-\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right.---\left(16\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(17\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_{Mj}\]\[C_{M-1,j}\]...\[C_{2j}\]\[C_{1j}\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(18\right),$

Above-mentioned formula (16), (17) and (18) is abbreviated as respectively:

$\left\{\begin{array}{c}{a}_{M0}\\ d_{M0}\end{array}\right\}=\left[\begin{array}{cc}1& \underset{i=1}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\\ 0& 1\end{array}\right]\left\{\begin{array}{c}{a}_{00}\\ d_{00}\end{array}\right\}+\left\{\begin{array}{c}-\underset{i=2}{\overset{M}{\mathrm{\Σ}}}\frac{1}{k_i}\left(\underset{k=1}{\overset{i-1}{\mathrm{\Σ}}}2m_{k}g\right)\\ -\underset{i=1}{\overset{M}{\mathrm{\Σ}}}2m_{i}g\end{array}\right\}---\left(19\right),$

$\left\{\begin{array}{c}{a}_{Mj}\\ d_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{a}_{0j}\\ d_{0j}\end{array}\right\},j=1,2,...,N---\left(20\right),$

$\left\{\begin{array}{c}{b}_{Mj}\\ e_{Mj}\end{array}\right\}=\[C_j\]\left\{\begin{array}{c}{b}_{0j}\\ e_{0j}\end{array}\right\},j=1,2,...,N---\left(21\right),$

For described diagnostic cast, the displacement function s of suspension point position₀=s₀(θ) solved by the motion analysis of oil pumper, axle power Function F₀=F₀(θ) obtained by interpolation according to displacement function and actual measurement polished rod indicator card；

Displacement function and axle force function are expanded into Fourier progression, it is thus achieved that coefficientWithThen the coefficient at pump is obtained by formula (19), (20) and (21)With

Obtaining the displacement function at pump by the calculating of Fourier level numerical expression (8), (9), (10) and (11) is: s_pump(θ)=- s_M；Axle force function is: F_pump(θ)=-F_M, i.e. the pump dynagraoph of sucker rod pump.

The method of water content in measurement oil well liquid-producing the most according to claim 3, it is characterised in that have described in step S4 The acquiring method of effect stroke is by polygonous approximation and vector characteristic method identification.

The method of water content in measurement oil well liquid-producing the most according to claim 4, it is characterised in that pump described in step S4 The merit area of pictural surface is:

$S={\∫}_{x_{\min }}^{x_{\max }}(F_u-F_d)dx---\left(22\right),$

In formula (22), F_u、F_dBe in a stroke cycle pumping unit horsehead through the load of same position pull bar Yu pump junction Lotus, x_min、x_maxIt is pull bar and the least displacement of pump junction point and maximum displacement.

The method of water content in measurement oil well liquid-producing the most according to claim 5, it is characterised in that in step S5, have bar Pump pump liquid within the cartridge gives rise to ground work done:

In formula (23), ρ_LiquidBeing oil well liquid-producing density, d is pump barrel internal diameter, and h is dynamic oil level, s_eIt it is pump effective stroke.

The method of water content in measurement oil well liquid-producing the most according to claim 6, it is characterised in that in step S6 in production fluid The acquiring method of water content is:

By: S=W (24),

ρ_Liquid=ρ_WaterV_Water+ρ_Oil(1-V_Water) (25),

ρ_WaterFor the density of water, ρ in oil well liquid-producing_OilFor the density of oil in oil well liquid-producing, can obtain:

Water content in formula (26) i.e. oil well liquid-producing.