CN104653455B - A kind of screw pump stator and the method for adjustment in rotor axial gap - Google Patents

Abstract

A kind of screw pump stator and the method for adjustment in rotor axial gap, belong to petroleum industry petroleum production engineering field.Containing the step measuring screw pump stator and rotor data, optimum as target with the length in rotor axial gap with screw pump stator, with coaxial double hollow oil pumping rod depth of setting, out temperature difference as constraints, set up the computation model of screw pump stator and the method for adjustment in rotor axial gap；Solve Mathematical Modeling numerical value；Obtain the adjustment length of screw pump stator and rotor axial gap；Adjust screw pump stator and rotor axial gap.Beneficial effects of the present invention: make screw pump stator simple, accurate with the lifting in rotor axial gap, completely avoid the generation of holddown phenomenon, substantially increase the one-stop operation success rate of screw bolt well.

Description

A kind of screw pump stator and the method for adjustment in rotor axial gap

Technical field

The present invention relates to the method for adjustment of a kind of screw pump stator and rotor axial gap, belong to petroleum industry petroleum production engineering Field.

Background technology

More successful and potential heavy oil cold flow production technology includes that Sand Production Cold Recovery, Vapex and chemical method are cold and adopts, screw pump There is continuous and stable pressure " window " and become heavy oil cold flow production lifting equipment and at home and abroad had many successfully reports, old The reddest et al. calculate sucker rod for screw pump well post elongation after, the dead space of proposition determine method make its promote simple, accurate, Holddown rate is almost nil.The screw pump cold special thick oil of adopting of supporting coaxial double hollow oil pumping rod attempted in recent years achieves successfully, but Because coaxial double hollow oil pumping rod diameter increases, heating it is increased by thermal expansion length, and screw pump stator adjusts with rotor axial gap Carry out by rule of thumb.

Summary of the invention

It is an object of the invention to: the method for adjustment of a kind of screw pump stator and rotor axial gap is provided, is beaten by single-point Target method calculates the adjustment length of screw pump stator and rotor axial gap.

A kind of screw pump stator and the method for adjustment in rotor axial gap, contain and measure screw pump stator and rotor data Step,

Data include: coaxial double hollow oil pumping rod depth of setting, out temperature are poor；

Screw pump stator and the length in rotor axial gap；In coaxial-type double hollow oil pumping rod, heat carrier softens the matter of water Amount；In coaxial-type double hollow oil pumping rod, heat carrier softens the flow rate of water；The circulation of circulation in coaxial-type double hollow oil pumping rod The pressure of water；Oil pipe cross-sectional area, coaxial-type double hollow oil pumping rod body radius；The every km of coaxial-type double hollow oil pumping rod Elongation, the elastic modelling quantity of coaxial-type double hollow oil pumping rod, the polar moment of inertia of coaxial-type double hollow oil pumping rod；

Also comprise the following steps that

Step 1: screw pump stator and the length Mathematical Models in rotor axial gap;

Coaxial double hollow oil pumping rod be a kind of have inside and outside the interior cycling hot conduction heating system of autonomous channel that seals against each other System, ground level heat interchanger is by the heating of the heat carrier such as water, conduction oil, anti-icing fluid, under the driving of circulating pump, double hollow takes out from coaxial The internal channel of beam hanger flows into external hollow passage after flowing at a high speed its lower end, dispels the heat and add the crude oil in oil pipe when outer tube returns Heat, last heat carrier returns to ground heat exchanger and again heats；With the length in screw pump stator and rotor axial gap Excellent for target, with coaxial double hollow oil pumping rod depth of setting, out temperature difference as constraints, set up screw pump stator and turn The computation model of the method for adjustment of sub-axial gap；

$\begin{array}{c}\mathrm{\Δt}(H,\mathrm{\Δt})=\frac{{6.78\mathrm{EIM}+\mathrm{Fr}}^2{k}_2}{{\left[A_c\mathrm{\πH\Δt}\right]}^{1/2}}\exp \{\frac{1+{\mathrm{Fr}}^2{k}_1}{16\mathrm{H\Δt}}+k_2\mathrm{\Δt}\}\left(\frac{\∂r}{\∂H}\right)+\\ \frac{k_2}{k_1\mathrm{\Σ}{k}_i}\·\frac{p_1+\mathrm{\Σ}{p}_i{p}_2}{\mathrm{\Σ}{p}_i}[1-\exp \left(\frac{r^2\mathrm{H\Δt}+{\mathrm{Fr}}^2{k}_2}{\mathrm{ETM}}\right)]\left(\frac{\∂r}{\∂H}\right)\end{array}---\left(1\right)$

In formula: H is the length of screw pump stator and rotor axial gap, m；Δ t is coaxial double hollow stem out temperature Difference (T₁-T₂, T₁For inlet temperature, T₂For outlet temperature), DEG C；M is heat carrier softening water in coaxial-type double hollow oil pumping rod Quality, kg/ km；K₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；ΣK_iTurn for first order kinetics Change speed, take 0.55～0.60；P₁For well mouth of oil well back pressure, MPa；P₂For the circulation of circulation in coaxial-type double hollow oil pumping rod The pressure of water, MPa；K₂For Henry's constant；Refer to O₂Henry's constant 4.40 × 10⁶；Σp_iFor distribution coefficient；Refer under uniform temperature, When being in poised state, water and air concentration in fixing mutually and the ratio of the concentration in flowing mutually；Ac is transversal in oil pipe Face area, mm²；R is coaxial-type double hollow oil pumping rod body radius, mm；F is the elongation of the every km of coaxial-type double hollow oil pumping rod Amount, m/ km；E is the elastic modelling quantity of double hollow oil pumping rod, Pa；I is the polar moment of inertia of double hollow oil pumping rod, m⁴；π is circumference Rate；

Step 2: set up constraints；

(1) coaxial double hollow stem out temperature difference is known, it may be assumed that Δ t=T₁-T₂, it may be assumed that the out temperature value of design, no The out temperature that same well requires is different；

(2) elongation of the every km of coaxial-type double hollow oil pumping rod is known, it may be assumed that F=0.923m/ km；

(3) elastic modulus E of double hollow oil pumping rod is known, it may be assumed that 3.2 × 10⁵Pa；

(4) polar moment of inertia I is it is known that i.e. 1.729 × 10^-3m⁴；

(5) in Ac is oil pipe, cross-sectional area is known, it may be assumed that external diameter 89mm pipe aperture is 76mm, cross-sectional area in it For: 4534.16mm²；

(6) r is that coaxial double hollow oil pumping rod body radius is known, it may be assumed that 22.5mm；In M is coaxial-type double hollow oil pumping rod Heat carrier softens the quality of water, kg/ km, it may be assumed that 600kg/ km;

(7) well mouth of oil well back pressure P₁, unit: MPa；Well mouth of oil well back pressure P₁Determination method: according to China National Petroleum Group company edit, China Plan Press publish, in August, 2005 first edition, National Standard of the People's Republic of China's oil gas collection Defeated design specification, GB50350-2005, page 10, during 4.1.3 design, oil well the highest permission back pressure is determined by following regulation: machine Tool producing well is preferably 1.0-1.5MPa；When the mechanical oil well of stripper field uses pipeline collection defeated, wellhead back pressure can be 1.0- 2.5MPa；

(8) P₂For the pressure of the recirculated water of circulation, MPa in coaxial-type double hollow oil pumping rod；Along with depth of setting not Different together, on-site measurement value；

(9) K₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；Take out along with coaxial-type pair is hollow The pressure of the recirculated water of circulation is different and different in beam hanger, on-site measurement value；

Step 3: Mathematical Modeling numerical solution；

Shooting method is to solve the method solving boundary value problem that reduction is an initial-value problem；Single-point shooting method is by implicit expression Border is explicitly changed as an object function, solves single argument nonlinear equation with one and tries to achieve the process of initial value；In (1) formula During middle H=0, Δ t=0, the elongation F of the every km of coaxial-type double hollow oil pumping rod is it is known that be equivalent to lack an initial value；Assume Double hollow stem out temperature difference Δ t=x are unknown variable, with initial value (H, x₁,x₂) to (1) formula integration, obtain Δ t during H=F Boundary value x₁(F)、x₂(F), because F it is known that so definition residual error function be:

Y(x)=H_in-H (F) (2)

As Y(x)=0 time, residual error function Y(x) cannot explicitly show, for given initial value (H, x₁,x₂) need Solve the differential equation and draw Y；For reducing the accumulation of error, use Fourth order Runge-Kutta gill form, for ensureing the steady of solution procedure The qualitative precision with numerical solution, takes step-length h≤20m, uses interative mtheod to ask the solution of nonlinear equation to obtain its root；Specifically solve Step is:

1. the functional value Y of (2) formula is sought₁、Y₂；

At closed interval [x_min, x_maxInitial value x is arbitrarily taken in]₁、x₂, and meet x_min≤x₁, x₂≤x_max, step units takes Δ x =0.5(x₂-x₁)；

2. Y(x is sought)=the approximation root of 0；

If Y₁Y₂＜ 0, obtains Y(x by linear interpolation method)=the approximation root of 0 is

$x=\frac{Y_2{x}_1-Y_1{x}_2}{Y_2-Y_1}$

Work as x=min{max{x_min, x}, x_maxTime, carry out step 4., otherwise carry out step 3.；

If 3. (Y₁-Y₂) Y₁＜ 0, updates x the most to the left₁、x₂Take

x₂=x₁,

x₁=max{x_min, x₁-Δx}；

If (Y₁-Y₂) Y1 ＞ 0, update the most to the right x₁、x₂Take

x₁=x₂

x₂=min{x₂+ Δ x, x_max}

Seek corresponding functional value Y₁、Y₂, and it is back to step 2., until meeting: Y₁Y₂＜ 0；

4. x linear interpolation obtained substitutes into (2) formula, obtains new functional value Y₃；

If 5. | Y₃| be not more than the computational accuracy set, then x is required root, carries out step 7.；If | Y₃| more than set 6. computational accuracy, carry out step；

If 6. (Y₁-Y₂) Y₃＞ 0, then x₁=x, Y₁=Y₃；If (Y₁-Y₂) Y₃＜ 0, then x₂=x, Y₂=Y₃；The x that interpolation is looked for novelty, and Carry out step 4.；

7. by (H, x₁,x₂) substitute into equation (1) solve, obtain the unique solution of Mathematical Modeling；

Step 4: obtain the adjustment length of screw pump stator and rotor axial gap；

Step 5: adjust screw pump stator and rotor axial gap.

Beneficial effects of the present invention: make screw pump stator simple, accurate with the lifting in rotor axial gap, completely avoid The generation of holddown phenomenon, substantially increases one-stop operation success rate and the production time efficiency of screw bolt well.Should at 15 mouthfuls of screw bolt wells With, one-stop operation success rate 100%.

Specific embodiment

As a example by X-67 well, the method that screw pump stator and the adjustment length in rotor axial gap are described.

Containing the step measuring screw pump stator and rotor data；

Data include: coaxial double hollow oil pumping rod depth of setting, out temperature are poor；

Screw pump stator and the length in rotor axial gap；In coaxial-type double hollow oil pumping rod, heat carrier softens the matter of water Amount, in coaxial-type double hollow oil pumping rod, heat carrier softens the flow rate of water；The circulation of circulation in coaxial-type double hollow oil pumping rod The pressure of water, oil pipe cross-sectional area, coaxial-type double hollow oil pumping rod body radius, the every km of coaxial-type double hollow oil pumping rod Elongation, the elastic modelling quantity of coaxial-type double hollow oil pumping rod, the polar moment of inertia of coaxial-type double hollow oil pumping rod；

Also comprise the following steps that

Step 1: screw pump stator and the length Mathematical Models in rotor axial gap;

Coaxial double hollow oil pumping rod be a kind of have inside and outside the interior cycling hot conduction heating system of autonomous channel that seals against each other System, ground level heat interchanger is by the heating of the heat carrier such as water, conduction oil, anti-icing fluid, under the driving of circulating pump, double hollow takes out from coaxial The internal channel of beam hanger flows into external hollow passage after flowing at a high speed its lower end, dispels the heat and add the crude oil in oil pipe when outer tube returns Heat, last heat carrier returns to ground heat exchanger and again heats；With the length in screw pump stator and rotor axial gap Excellent for target, with coaxial double hollow oil pumping rod depth of setting, out temperature difference as constraints, set up screw pump stator and turn The computation model of the method for adjustment of sub-axial gap；

$\begin{array}{c}\mathrm{\Δt}(H,\mathrm{\Δt})=\frac{{6.78\mathrm{EIM}+\mathrm{Fr}}^2{k}_2}{{\left[A_c\mathrm{\πH\Δt}\right]}^{1/2}}\exp \{\frac{1+{\mathrm{Fr}}^2{k}_1}{16\mathrm{H\Δt}}+k_2\mathrm{\Δt}\}\left(\frac{\∂r}{\∂H}\right)+\\ \frac{k_2}{k_1\mathrm{\Σ}{k}_i}\·\frac{p_1+\mathrm{\Σ}{p}_i{p}_2}{\mathrm{\Σ}{p}_i}[1-\exp \left(\frac{r^2\mathrm{H\Δt}+{\mathrm{Fr}}^2{k}_2}{\mathrm{ETM}}\right)]\left(\frac{\∂r}{\∂H}\right)\end{array}---\left(1\right)$

In formula: H is the length of screw pump stator and rotor axial gap, m；Δ t is coaxial double hollow stem out temperature Difference (T₁-T₂, T₁For inlet temperature, T₂For outlet temperature), DEG C；M is heat carrier softening water in coaxial-type double hollow oil pumping rod Quality, kg/ km；K₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；ΣK_iTurn for first order kinetics Change speed, take 0.55～0.60；P₁For well mouth of oil well back pressure, MPa；P₂For the circulation of circulation in coaxial-type double hollow oil pumping rod The pressure of water, MPa；K₂For Henry's constant；Refer to O₂Henry's constant 4.40 × 10⁶；Σp_iFor distribution coefficient；Refer under uniform temperature, When being in poised state, water and air concentration in fixing mutually and the ratio of the concentration in flowing mutually；Ac is transversal in oil pipe Face area, mm²；R is coaxial-type double hollow oil pumping rod body radius, mm；F is the elongation of the every km of coaxial-type double hollow oil pumping rod Amount, m/ km；E is the elastic modelling quantity of double hollow oil pumping rod, Pa；I is the polar moment of inertia of double hollow oil pumping rod, m⁴；π is circumference Rate；

Step 2: set up constraints；

(1) coaxial double hollow stem out temperature difference is known, it may be assumed that Δ t=T₁-T₂, T₁It is 85 DEG C, T₂It it is 55 DEG C；

(2) elongation of the every km of coaxial-type double hollow oil pumping rod is known, it may be assumed that F=0.923m/ km；

(3) elastic modulus E of double hollow oil pumping rod is known, it may be assumed that 3.2 × 10⁵Pa；

(4) polar moment of inertia I is it is known that i.e. 1.729 × 10^-3m⁴；

(5) in Ac is oil pipe, cross-sectional area is known, it may be assumed that external diameter 89mm pipe aperture is 76mm, cross-sectional area in it For: 4534.16mm²；

(6) r is that coaxial double hollow oil pumping rod body radius is known, it may be assumed that 22.5mm；

(7) in M is coaxial-type double hollow oil pumping rod, heat carrier softens the quality of water, kg/ km, it may be assumed that 600kg/ km;

(8) well mouth of oil well back pressure P₁, unit: MPa；Well mouth of oil well back pressure P₁Determination method: according to China National Petroleum Group company edit, China Plan Press publish, in August, 2005 first edition, National Standard of the People's Republic of China's oil gas collection Defeated design specification, GB50350-2005, page 10, during 4.1.3 design, oil well the highest permission back pressure is determined by following regulation: machine Tool producing well is preferably 1.0-1.5MPa；When the mechanical oil well of stripper field uses pipeline collection defeated, wellhead back pressure can be 1.0- 2.5MPa；

(9) P₂For the pressure of the recirculated water of circulation, MPa in coaxial-type double hollow oil pumping rod；Along with depth of setting not Different together, on-site measurement value；

(10) K₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；Take out along with coaxial-type pair is hollow The pressure of the recirculated water of circulation is different and different in beam hanger, on-site measurement value；

(11) Σ K_iFor first order kinetics conversion rate, take 0.55～0.60；Take 0.55；

(12) K₂For Henry's constant；Refer to the Henry's constant 4.40 × 10 of O2⁶；

(13) Σ p_iFor distribution coefficient；Refer under uniform temperature, when being in poised state, dense in fixing mutually of water and air Degree and the ratio of the concentration in flowing mutually, take 1.0；

Step 3: Mathematical Modeling numerical solution；

Shooting method is to solve the method solving boundary value problem that reduction is an initial-value problem；Single-point shooting method is by implicit expression Border is explicitly changed as an object function, solves single argument nonlinear equation with one and tries to achieve the process of initial value；In (1) formula During middle H=0, Δ t=0, the elongation F of the every km of coaxial-type double hollow oil pumping rod is it is known that be equivalent to lack an initial value；Assume Double hollow stem out temperature difference Δ t=x are unknown variable, with initial value (H, x₁,x₂) to (1) formula integration, obtain Δ t during H=F Boundary value x₁(F)、x₂(F), because F it is known that so definition residual error function be:

Y(x)=H_in-H (F) (2)

As Y(x)=0 time, residual error function Y(x) cannot explicitly show, for given initial value (H, x₁,x₂) need Solve the differential equation and draw Y；For reducing the accumulation of error, use Fourth order Runge-Kutta gill form, for ensureing the steady of solution procedure The qualitative precision with numerical solution, takes step-length h≤20m, uses interative mtheod to ask the solution of nonlinear equation to obtain its root；Specifically solve Step is:

4. the functional value Y of (2) formula is sought₁、Y₂；

At closed interval [x_min, x_maxInitial value x is arbitrarily taken in]₁、x₂, and meet x_min≤x₁, x₂≤x_max, step units takes Δ x =0.5(x₂-x₁)；

5. Y(x is sought)=the approximation root of 0；

If Y₁Y₂＜ 0, obtains Y(x by linear interpolation method)=the approximation root of 0 is

$x=\frac{Y_2{x}_1-Y_1{x}_2}{Y_2-Y_1}$

Work as x=min{max{x_min, x}, x_maxTime, carry out step 4., otherwise carry out step 3.；

If 6. (Y₁-Y₂) Y₁＜ 0, updates x the most to the left₁、x₂Take

x₂=x₁,

x₁=max{x_min, x₁-Δx}；

If (Y₁-Y₂) Y1 ＞ 0, update the most to the right x₁、x₂Take

x₁=x₂

x₂=min{x₂+ Δ x, x_max}

Seek corresponding functional value Y₁、Y₂, and it is back to step 2., until meeting: Y₁Y₂＜ 0；

4. x linear interpolation obtained substitutes into (2) formula, obtains new functional value Y₃；

If 5. | Y₃| be not more than the computational accuracy set, then x is required root, carries out step 7.；If | Y₃| more than set 6. computational accuracy, carry out step；

If 6. (Y₁-Y₂) Y₃＞ 0, then x₁=x, Y₁=Y₃；If (Y₁-Y₂) Y₃＜ 0, then x₂=x, Y₂=Y₃；The x that interpolation is looked for novelty, and Carry out step 4.；

7. by (H, x₁,x₂) substitute into equation (1) solve, obtain the unique solution of Mathematical Modeling；

Step 4: obtain the adjustment length of screw pump stator and rotor axial gap；

1) when coaxial double hollow oil pumping rod depth of setting is 800m, screw pump stator is long with the adjustment in rotor axial gap Degree is 1.20m；

2) when coaxial double hollow oil pumping rod depth of setting is 900m, screw pump stator is long with the adjustment in rotor axial gap Degree is 1.29m；

3) when coaxial double hollow oil pumping rod depth of setting is 1000m, screw pump stator and the adjustment in rotor axial gap A length of 1.40m；

4) when coaxial double hollow oil pumping rod depth of setting is 1100m, screw pump stator and the adjustment in rotor axial gap A length of 1.40m；

5) when coaxial double hollow oil pumping rod depth of setting is 1200m, screw pump stator and the adjustment in rotor axial gap A length of 1.80m；

5) when coaxial double hollow oil pumping rod depth of setting is 1300m, screw pump stator and the adjustment in rotor axial gap A length of 2.10m；

Step 5: adjust screw pump stator and rotor axial gap.

X-67 well coaxial double hollow oil pumping rod depth of setting depth of setting 1200m, screw pump stator and rotor axial gap The a length of 1.80m of adjustment；Bring in once success.

Other apply the screw bolt well screw pump stator adjustment length with rotor axial gap of coaxial double hollow oil pumping rod Method, identical with this, do not describing in detail.

Described screw pump stator is the normal dead space said with in rotor axial gap i.e. industry.

As it has been described above, embodiments of the invention are explained, but as long as essentially without departing from this Bright inventive point and effect can have a lot of deformation, and this will be readily apparent to persons skilled in the art.Therefore, this Within the variation of sample is also integrally incorporated in protection scope of the present invention.

Claims (1)

1. a screw pump stator and the method for adjustment in rotor axial gap, it is characterised in that containing measuring screw pump stator and turning The step of subdata；

Data include: coaxial double hollow oil pumping rod depth of setting, out temperature are poor；Dead space length；Coaxial-type pair is hollow takes out In beam hanger, heat carrier softens the water yield of water, and in coaxial-type double hollow oil pumping rod, heat carrier softens the flow rate of water；Coaxial-type is double The pressure of the recirculated water of circulation in hollow rod, oil pipe cross-sectional area, coaxial-type double hollow oil pumping rod body radius, coaxially The elongation of the every km of formula double hollow oil pumping rod, the polar moment of inertia of the elastic modelling quantity double hollow oil pumping rod of double hollow oil pumping rod；

Also comprise the following steps that

Step 1: screw pump stator and the length Mathematical Models in rotor axial gap；

Coaxial double hollow oil pumping rod be a kind of have inside and outside the interior cycling hot conduction heating system of autonomous channel that seals against each other, ground Heat exchanger is by water, conduction oil, the heating of anti-icing fluid heat carrier, under the driving of circulating pump, from coaxial double hollow oil pumping rod Internal channel flows into external hollow passage after flowing at a high speed its lower end, and when outer tube returns, heat radiation is to the heating crude oil in oil pipe, finally Heat carrier returns to ground heat exchanger and again heats；Optimum as mesh with the length in rotor axial gap with screw pump stator Mark, with coaxial double hollow oil pumping rod depth of setting, out temperature difference as constraints, sets up screw pump stator and rotor axial The computation model of the method for adjustment in gap；

$\begin{array}{c}\mathrm{\Δ}t(H,\mathrm{\Δ}t)=\frac{6.78EIM+{\mathrm{Fr}}^2{k}_2}{{\[A_c\mathrm{\π}H\mathrm{\Δ}t\]}^{1/2}}\exp \left\{\frac{1+{\mathrm{Fr}}^2{k}_1}{16H\mathrm{\Δ}t}+k_2\mathrm{\Δ}t\right\}\left(\frac{\∂r}{\∂H}\right)+\\ \frac{k_2}{k_1\Σk_i}\·\frac{p_1+\Σp_i{p}_2}{\Σp_i}\[1-\exp \left(\frac{r^{2}H\mathrm{\Δ}t+{\mathrm{Fr}}^2{k}_2}{ETM}\right)\]\left(\frac{\∂r}{\∂H}\right)\end{array}---\left(1\right)$

In formula: H is the length of screw pump stator and rotor axial gap, m；Δ t is that coaxial double hollow stem out temperature is poor (T₁-T₂, T₁For inlet temperature, T₂For outlet temperature), DEG C；M is the matter that heat carrier softens water in coaxial-type double hollow oil pumping rod Amount, kg/ km；k₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；Σk_iConvert for first order kinetics Speed, takes 0.55～0.60；p₁For well mouth of oil well back pressure, MPa；p₂For the recirculated water of circulation in coaxial-type double hollow oil pumping rod Pressure, MPa；k₂For Henry's constant；Refer to O₂Henry's constant 4.40 × 10⁶；Σp_iFor distribution coefficient；Refer under uniform temperature, place When poised state, water and air concentration in fixing mutually and the ratio of the concentration in flowing mutually；Ac is cross section in oil pipe Area, mm²；R is coaxial-type double hollow oil pumping rod body radius, mm；F is the elongation of the every km of coaxial-type double hollow oil pumping rod Amount, m/ km；E is the elastic modelling quantity of double hollow oil pumping rod, Pa；I is the polar moment of inertia of double hollow oil pumping rod, m⁴；π is circumference Rate；

Step 2: set up constraints；

(1) coaxial double hollow stem out temperature difference is known, it may be assumed that Δ t=T₁-T₂, it may be assumed that the out temperature value of design is different Well require out temperature be different；

(2) elongation of the every km of coaxial-type double hollow oil pumping rod is known, it may be assumed that F=0.923m/ km；

(3) elastic modulus E of double hollow oil pumping rod is known, it may be assumed that 3.2 × 10⁵Pa；

(4) polar moment of inertia I is it is known that i.e. 1.729 × 10^-3m⁴；

(5) in Ac is oil pipe, cross-sectional area is known, it may be assumed that external diameter 89mm, and pipe aperture is 76mm, and in it, cross-sectional area is: 4534.16mm²；

(6) r is that coaxial double hollow oil pumping rod body radius is known, it may be assumed that 22.5mm；M is heat load in coaxial-type double hollow oil pumping rod Body softens the quality of water, kg/ km, it may be assumed that 600kg/ km；

(7) well mouth of oil well back pressure p₁, unit: MPa；Well mouth of oil well back pressure p₁Determination method: according to China National Petroleum group Company edit, China Plan Press publish, in August, 2005 first edition, National Standard of the People's Republic of China's oil-gas gathering and transportation sets Meter specification, GB50350-2005, page 10, during 4.1.3 design, oil well the highest permission back pressure is determined by following regulation: machinery is adopted Oil well is 1.0-1.5MPa；When the mechanical oil well of stripper field uses pipeline collection defeated, wellhead back pressure can be 1.0-2.5MPa；

(8)p₂For the pressure of the recirculated water of circulation, MPa in coaxial-type double hollow oil pumping rod；Along with depth of setting difference and not With, on-site measurement value；

(9)k₁The flow rate of water is softened for heat carrier in coaxial-type double hollow oil pumping rod；Along with in coaxial-type double hollow oil pumping rod The pressure of the recirculated water of circulation is different and different, on-site measurement value；

Step 3: Mathematical Modeling numerical solution；

Shooting method is to solve the method solving boundary value problem that reduction is an initial-value problem；Single-point shooting method is by implicit expression border Explicitly change as an object function, solve single argument nonlinear equation with one and try to achieve the process of initial value；H in (1) formula When=0, Δ t=0, the elongation F of the every km of coaxial-type double hollow oil pumping rod is it is known that be equivalent to lack an initial value；Assume Double hollow stem out temperature difference Δ t=x are unknown variable, with initial value (H, x₁,x₂) to (1) formula integration, obtain Δ during H=F The boundary value x of t₁(F)、x₂(F), because F it is known that so definition residual error function be:

Y (x)=H_in-H(F) (2)

When Y (x)=0, residual error function Y (x) cannot explicitly show, for given initial value (H, x₁,x₂) need to solve micro- Equation is divided to draw Y；For reducing the accumulation of error, use Fourth order Runge-Kutta gill form, for ensureing the stability of solution procedure With the precision of numerical solution, take step-length h≤20m, use interative mtheod to ask the solution of nonlinear equation to obtain its root；Concrete solution procedure For:

8. the functional value Y of (2) formula is sought₁、Y₂；

At closed interval [x_min, x_maxInitial value x is arbitrarily taken in]₁、x₂, and meet x_min≤x₁, x₂≤x_max, step units takes Δ x=0.5 (x₂-x₁)；

9. the approximation root of Y (x)=0 is sought；

If Y₁Y₂＜ 0, the approximation root obtaining Y (x)=0 by linear interpolation method is

Work as x=min{max{x_min, x}, x_maxTime, carry out step 4., otherwise carry out step 3.；

If 10. (Y₁-Y₂)Y₁＜ 0, updates x the most to the left₁、x₂Take

x₂=x₁,

x₁=max{x_min, x₁-Δx}；

If (Y₁-Y₂) Y1 ＞ 0, update the most to the right x₁、x₂Take

x₁=x₂

x₂=min{x₂+ Δ x, x_max}

Seek corresponding functional value Y₁、Y₂, and it is back to step 2., until meeting: Y₁Y₂＜ 0；

4. x linear interpolation obtained substitutes into (2) formula, obtains new functional value Y₃；

If 5. | Y₃| be not more than the computational accuracy set, then x is required root, carries out step 7.；If | Y₃| more than the calculating set 6. precision, carry out step；If 6. (Y₁-Y₂)Y₃＞ 0, then x₁=x, Y₁=Y₃；If (Y₁-Y₂)Y₃＜ 0, then x₂=x, Y₂=Y₃；Insert The x that value is looked for novelty, and carry out step 4.；

7. by (H, x₁,x₂) substitute into equation (1) solve, obtain the unique solution of Mathematical Modeling；

Step 4: obtain the adjustment length of screw pump stator and rotor axial gap；

Step 5: adjust screw pump stator and rotor axial gap.