CN1282818C - Prediction method, control method and control system for horizontal well drill bit advancing direction - Google Patents

Abstract

A prediction and control method and a control system for the advancing direction of a drilling bit of an offshore horizontal well form a virtual actual working condition of drilling engineering mainly according to design parameters of drilling and measured well track parameters; dividing the formed virtual drill string into a plurality of units, wherein two ends of each unit are nodes; determining an integral node force vector and an integral node displacement vector of the drill string according to a nonlinear finite element method; determining real contact points of each node of the virtual drill string and the virtual well wall; determining the future drilling direction of the drill bit according to the axial force and the lateral force at the drill bit; and comparing the data related to the future drilling direction of the drill bit with the original well track design data, and sending an instruction to the near drill bit stabilizer according to the comparison result, so that the drilling direction of the drill bit can be corrected, and the drill bit can be guaranteed to drill according to the original design track.

Description

The Forecasting Methodology of horizontal well drill bit advancing direction, control method and control system thereof

Technical field

The present invention relates to the prediction and the control thereof of the following motion state of a kind of horizontal well drill bit, more particularly, relate to Forecasting Methodology, control method and the control system thereof of a kind of coastal waters horizontal well Drilling bore bit direction of advance.

Background technology

At oil circle, because horizontal well reduces production costs improving oil well output, the remarkable effect of marginal field development and aspect, complex area oil field, the drilling hole number of horizontal well is more and more in recent years.In theoretical circles, research to the horizontal well frictional resistance also reaches its maturity, an outstanding feature is that existing many experts and scholars have noticed horizontal well, the nonlinear characteristic of especially big level of displacement and mechanics is (referring to J.L.Thorogood, Amathematics model for analysis drilling performance and estimatingwell times, SPE 16524/1 (1994), 445-449).Yet when research level well non-linear force mathematic(al) parameter, the non-linear frictional resistance moment of torsion research of drill string was seldom studied still less the drill bit advancing direction under the suffered non-linear force state of drill string during people crept into horizontal well.Existing linear prediction method calculates more coarse, and the accuracy of controlling that predicts the outcome of therefore utilizing linear prediction method and being obtained is difficult for satisfying requirement of engineering, and can not consider because horizontal well creeps into how much large deformation problems that brought.

What the used rig of present offshore oil adopted is " top drive " rig, all is furnished with accurate drill string torductor for every.Under the situation of more complete situ hardware and actual well drilled technical need, the inventor works having done for many years aspect prediction and the monitoring drill string moment of torsion.On prediction theory, from the prediction of linear moment of torsion develop into nonlinear prediction (referring to Guo Yongfeng, Lv Yingmin. the nonlinear analysis research of horizontal well drill string frictional resistance. oil drilling technology, 1996,18 (2): 14-17.).As for the prediction and the control of the following direction of drill bit, also be that all to be equipped with MWD (Measure WhileDrilling measurement-while-drilling system) relevant with offshore oil drilling platform.The every survey data of the drill bit that utilizes this system to provide is passed through the computing of computer program again, can provide the parameter of the following motion state of drill bit at any time for wellbore construction department, so that control the direction of advance of actual drill bit.Original nonlinear method can not solve contact nonlinear problem preferably, so the following direction of the drill bit in being difficult for determining exactly to creep into.The method of prediction and control drill bit advancing direction when up to the present still not being implemented in prediction level well frictional resistance.

Summary of the invention

Purpose of the present invention just provides the nonlinear prediction method of a kind of coastal waters horizontal well Drilling bore bit direction of advance, and it can dope the direction that the suffered moment of torsion of horizontal well drill string and drill bit will advance future more accurately.

Another object of the present invention provides the control method of a kind of coastal waters horizontal well Drilling bore bit direction of advance, and it can adjust the actual direction of advance of drill bit in the horizontal well drilling process more exactly according to the design direction of drill bit.

A further object of the present invention provides the control system of a kind of coastal waters horizontal well Drilling bore bit direction of advance, and it can realize the control method of coastal waters of the present invention horizontal well Drilling bore bit direction of advance.

For this reason, the invention provides the nonlinear prediction method of a kind of coastal waters horizontal well Drilling bore bit direction of advance, may further comprise the steps: the design parameters of input drilling well, comprise the drill string total length, full well well depth, borehole diameter, drill string internal diameter, the drill string external diameter, casing inner diameter, cover external diameter of pipe, the friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density etc.; Measure the well trajectory parameters, comprise well depth, hole angle, the azimuth of well track each point; Utilize the well track parameter of above-mentioned design parameters and measurement to form virtual drilling engineering actual condition; Formed drill string is divided into a plurality of unit, and the two ends of this unit are node; Determine the whole displacement of joint vector of whole joint forces vector sum of drill string according to nonlinear finite element method; Determine the real contact point of each node of drill string and the borehole wall; Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future.

The present invention also provides the control method of a kind of coastal waters horizontal well Drilling bore bit direction of advance, may further comprise the steps: the design parameters of input drilling well comprises the drill string total length, full well well depth, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, the cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density etc.; Measure the well trajectory parameters, comprise well depth, hole angle, the azimuth of well track each point; Utilize the well track parameter of above-mentioned design parameters and measurement to form virtual drilling engineering actual condition; Formed drill string is divided into a plurality of unit, and the two ends of this unit are node; Determine the whole displacement of joint vector of whole joint forces vector sum of drill string according to nonlinear finite element method; Determine the real contact point of each node of drill string and the borehole wall; Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future; Data and original well track design data about the drilling direction in drill bit future are compared, send instruction according to comparative result to near-bit stabilizer, in order to revise the drill bit drilling direction, to ensure that drill bit creeps into by original planned course.

According to the present invention, the control system of a kind of coastal waters horizontal well Drilling bore bit direction of advance also is provided, comprising: control device; Well-drilling borehole trajectory measurement device is used to measure the well-drilling borehole trajectory parameters, comprising well depth, hole angle, the azimuth of well track each point; The design parameters input unit, be used for design parameters, comprise the drill string total length, full well well depth to control device input drilling well, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, the cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density; Signal receiving device is used to receive the control signal of described control device, and control can change the control attitude of the near-bit stabilizer of drill bit drilling direction; Wherein, described control device receives the well-drilling borehole trajectory parameters of well-drilling borehole trajectory measurement measurement device and the design parameters of this drilling well that the design parameters input unit is imported, and forms virtual drilling engineering actual condition; Formed drill string is divided into a plurality of unit, and the two ends of this unit are node; Determine the whole displacement of joint vector of whole joint forces vector sum of drill string according to nonlinear finite element method; Determine the real contact point of each node of drill string and the borehole wall; Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future; Data and original well track design data about the drilling direction in drill bit future are compared, send instruction according to comparative result to signal receiving device, in order to revise the drill bit drilling direction, to ensure that drill bit creeps into by original planned course.

Utilization is crept into the moment of torsion that the nonlinear prediction method of friction torque obtained according to coastal waters of the present invention horizontal well and is predicted the outcome very approaching with the trend of actual drilling process, therefore, utilize this to predict the outcome actual drilling process controlled and to obtain good effect.This point for the generation degree of depth of estimating peak torque before horizontal well spuds in, is carried out the preparation that prevents bit freezing in advance, is equipped with the rig power of big power reserve coefficient, all is significant.

Utilization has reached 78.9% according to the nonlinear prediction method of coastal waters of the present invention horizontal well drill bit advancing direction to the predictablity rate of drill bit direction of deflection, and the predictablity rate of drill bit azimuth direction has reached 57.1%.

Description of drawings

Fig. 1 a shows drill string mechanics fundamental coordinate system and well curve;

Fig. 1 b shows the motion vector on unit, the discrete back of the drill string node;

Fig. 2 shows the block diagram that creeps into the Forecasting Methodology of friction torque and drill bit advancing direction according to coastal waters of the present invention horizontal well;

Fig. 3 shows the block diagram according to the control method of drill bit advancing direction in the horizontal well drilling process of coastal waters of the present invention;

Fig. 4 shows the block diagram according to the control system of drill bit advancing direction in the horizontal well drilling process of coastal waters of the present invention;

Fig. 5 has expressed the contrast situation of nonlinear prediction moment of torsion with the actual measurement moment of torsion of this well with the mode of curve;

Fig. 6 has expressed the contrast situation of linear prediction moment of torsion with the actual measurement moment of torsion of this well with the mode of curve.

The specific embodiment

At first basic principle of the present invention is introduced.

With the horizontal well is example, and getting full well drill string is research object, and drill string can be considered elongated any space curve reinforcing beam in well, and its coordinate system is seen Fig. 1 (a).Use Finite Element Method, utilize following formula that drill string is separated into many straight beam junior units along axis;

$L=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{l}_i---\left(1\right)$

Wherein L is a drill string total length in the full hole, l _iBe the drill string length of i junior unit, n is the junior unit sum that whole drill string is divided, and two end points of each junior unit are called node, and wherein the coordinate system of each straight beam element and motion vector are shown in Fig. 1 (b).On this basis, set up the unit equilibrium equation, as formula (2).

[k]{q}＝{f} (2)

Wherein

[k] is the unit nonlinear stiffness matrix; { q} is a unit displacement of joint vector; { f} is a unit joint forces vector;

The displacement of joint vector of unit is

{q}＝[q _i，q _j] ^T＝

＝[u _i，v _i，w _i，θ _xi，θ _yi，θ _zi，u _j，v _j，w _j，θ _xj，θ _yj，θ _zj] ^T

(3)

Wherein, u _iX axis displacement for unit i node; v _iBe the Y direction displacement of unit i node, w _iBe the Z direction displacement of unit i node, θ _XiBe the corner of unit i node around X-axis, θ _YiBe the corner of unit i node around Y-axis, θ _ZiBe the corner of unit i node around the Z axle; u _jX axis displacement for unit j node; v _jBe the Y direction displacement of unit j node, w _jBe the Z direction displacement of unit j node, θ _XjBe the corner of unit j node around X-axis, θ _YjBe the corner of unit j node around Y-axis, θ _ZjBe the corner of unit j node around the Z axle.

The joint forces vector of unit is

{f}＝[f _i，f _j] ^T＝[n _xi，p _yi，p _zi，m _xi，m _yi，m _zi，n _xj，p _yj，p _zj，m _xj，m _yj，m _zj] ^T

(4)

Wherein, n _XiX axis power for unit i node; p _YiBe the Y direction component of unit i node, p _ZiBe the Z direction component of unit i node, m _XiBe the moment of torsion of unit i node around X-axis, m _YiBe the moment of flexure of unit i node around Y-axis, m _ZiBe the moment of flexure of unit i node around the Z axle; n _XjX axis power for unit j node; p _YjBe the Y direction component of unit j node, p _ZjBe the component of the Z direction of unit j node, m _XjBe the moment of torsion of unit j node around X-axis, m _YjBe the moment of flexure of unit j node around Y-axis, m _ZjBe the moment of flexure of unit j node around the Z axle.

On the basis of said units equilibrium equation, the method with structural mechanics assembles the integral rigidity matrix with all element stiffness matrixs, obtains finite element fundamental equation group and is

[K]{Q}＝{F} (5)

Wherein

[K] is whole nonlinear stiffness matrix; { Q} is whole displacement of joint vector; { F} is whole joint forces vector.

Utilize " wave-front method " to find the solution this large-scale equation group and can draw stressed (comprise axial force, lateral force, moment of torsion and moment of flexure etc.) of underground drill stem on each cross section and the displacement on each cross section (comprising axial displacement, lateral displacement, windup-degree, angle of bend etc.).

The representation of formula (5) is equivalent to " Hooke's law " in the foundation of physics, promptly does the time spent when single-ended fixing spring other end is stressed, and the pass of its active force and spring one end movement is:

σ＝Eε (5)’

Wherein σ is the suffered active force of spring one end; ε is the displacement that this end of spring causes because of active force, and E is the intrinsic modulus of elasticity of spring.

By (5) ' formula contrast (5) formula, the left side of (5) formula is the displacement of drill string as can be known, the right is the suffered active force of drill string.So the primary condition of substitution drill string in well just can be obtained corresponding displacement (comprising axial displacement, lateral displacement, windup-degree, angle of bend etc.) by (5) formula, and active force (comprising axial force, lateral force, moment of torsion and moment of flexure etc.).

In well, because the drill string distortion is subjected to the restriction of borehole diameter size, so the displacement of each node will satisfy condition

|φ _i|≤Δ _i (6)

Wherein,

φ _iDisplacement { Q for i node of drill string _iIn displacement projection perpendicular to the borehole axis direction; { Q wherein _iBe { the displacement summation of Q} displacement array on i node;

Δ _iBe the drill string of i node of drill string and the displacement restriction amount between the borehole wall.

Formula (5) and formula (6) have constituted a contact nonlinear problem.This contact nonlinear problem can be resolved by iterative formula (5) and formula (6), thereby obtains full well drill string and the borehole wall nonlinear contact power at each point.

Below the basic calculating formula of finding the solution the drill string friction torque is described.

After solving the full well drill string and the borehole wall nonlinear contact power, obtain drill string suffered non-linear friction resistance and friction torque from following formula at each point:

R＝{μ} ^T·{F} (8)

M＝μ·{r} ^T·{F} (9)

Wherein

{ F} is the whole joint forces array of drill string; { μ } is the friction factor array between the drill string and the borehole wall; { r} is that the practical function radius array R of drill string and each contact point of the borehole wall is a drill string non-linear axial frictional resistance; M is the drill string friction torque.The purpose of obtaining suffered non-linear friction resistance of drill string and friction torque is to provide possibility for accurately predicting drill bit drilling direction, because the drill bit direction is to be derived by the axial force at drill bit place and lateral force, and each power at drill bit place is to be come by the power recursion at each node place of drill string.

Point out in passing in iterative process, above the size and the direction of the non-linear axial frictional resistance obtained, all influential to the non-linear friction moment of torsion of drill string.In view of this, more than asking the process of axial rub resistance, also is the process that constantly iterates.

Introduce the method for drill bit advancing direction of finding the solution below.

With the instantaneous axis in per moment of drill string in the well, set up dynamic coordinate, the coordinate that promptly moves about is with reference to Fig. 1 (a).If the axial force of shaft bottom drill bit is τ, the lateral force of the direction of deflection that drill bit is suffered is η, and the lateral force of azimuth direction is ξ, and wherein, τ, ξ, η are the whole joint forces array of the drill string { component of F}.Getting drill bit and shaft bottom end points is basic point, and then drill bit is respectively at the π with joint efforts on hole deviation plane with at the ω that makes a concerted effort of aximuthpiston:

π＝τ+η (10)

ω＝τ+ξ (11)

More than each parameter be vector, two formulas also are all vector and formula.Consider stratigraphic dip, the anisotropy on stratum, and " conformality " of different model drill bit, the azimuthal angle beta in the deflecting direction angle alpha in final drill bit future and drill bit future is:

α＝λ(τ，π) (12)

β＝γ(τ，ω) (13)

In a preferred embodiment of the invention, α and β are respectively:

$\mathrm{\α}=\mathrm{arctg}\frac{\mathrm{k\η}}{\mathrm{\τ}}---\left(14\right)$

$\mathrm{\β}=\mathrm{arctg}\frac{\mathrm{k\ξ}}{\mathrm{\τ}}---\left(15\right)$

Wherein k is obtained by following formula:

$\frac{\mathrm{\τ}}{\mathrm{\π}}=\ln \frac{\sqrt{1-k^2}}{k}+\sqrt{1-k^2}---\left(16\right)$

In formula (12) and formula (13), λ and γ are respectively hole angle and the azimuthal correction factors behind the consideration various factors.Generally speaking, the general absolute value in drill bit advancing direction angle is very little, and its positive and negative difference represented diametrically opposite engineering significance, and this has just determined to find the solution the arduousness of this parameter.Obtain the key of the following direction of drill bit more exactly, be to use the duty of the whole drill string of computer simulation in well, and more accurately obtain the building force and the orientation power at drill bit place thus; Say that with mathematical linguistics all drill string mechanics parameters all must be calculated on the basis and drawn full well drill string being carried out nonlinear iteration, so just may have Practical significance.

Owing to compare with general drilling process, the drill string of extended horizontal well is in bigger elastic deformation all the time, so the element stiffness matrix [k] in the formula (2), its mathematical derivation process must consider that the nonlinear geometry of drill string unit after stressed is out of shape.Therefore, by theory of elastic mechanics, with reference to Fig. 1 b, after we supposed the stressed effect distortion in three-dimensional drill string unit, its strain can be divided into three parts, the one, tension and compression strain stress _a, two are perpendicular to the bending strain ε on the xy plane on the axis direction _b, three are perpendicular to the bending strain ε on the xz plane on the axis direction _c, and reverse shearing strain ε _dBe with matrix notation:

$\mathrm{\ϵ}=\left[\begin{array}{c}{\mathrm{\ϵ}}_a\\ {\mathrm{\ϵ}}_b\\ {\mathrm{\ϵ}}_c\\ {\mathrm{\ϵ}}_d\end{array}\right]---\left(17\right)$

In fact, following formula is made up of linear strain and nonlinear strain two parts, is

$\mathrm{\ϵ}=\left[\begin{array}{c}\frac{\mathrm{du}}{\mathrm{dx}}\\ -y\frac{d^{2}v}{d{x}^2}\\ -z\frac{d^{2}w}{d{x}^2}\\ r\frac{\mathrm{d\θ}}{\mathrm{dx}}\end{array}\right]+\frac{1}{2}\left[\begin{array}{c}{\left(\frac{\mathrm{du}}{\mathrm{dx}}\right)}^2+{\left(\frac{\mathrm{dv}}{\mathrm{dx}}\right)}^2+{\left(\frac{\mathrm{dw}}{\mathrm{dx}}\right)}^2\\ 3y\frac{d^{2}v}{d{x}^2}{\left(\frac{\mathrm{dv}}{\mathrm{dx}}\right)}^2-\frac{15}{4}y\frac{d^{2}v}{d{x}^2}{\left(\frac{\mathrm{dv}}{\mathrm{dx}}\right)}^4\\ 3z\frac{d^{2}w}{d{x}^2}{\left(\frac{\mathrm{dw}}{\mathrm{dx}}\right)}^2-\frac{15}{4}z\frac{d^{2}w}{d{x}^2}{\left(\frac{\mathrm{dw}}{\mathrm{dx}}\right)}^4\\ 0\end{array}\right]---\left(18\right)$

More than be the Basic Optical Formula that non-linear drill string element stiffness matrix is derived.This equation is to traditional Elasticity method, and Taloy (Taylor) expansion in the utilization higher mathematics is launched to form.

Following formula is the strain expression formula behind the drill string stress deformation from physical significance, and wherein the high-order nonlinear item is that the inventor independently derives.When this formula is used for horizontal drilling, can in calculating, considers the drill string large deformation problem that causes owing to horizontal drilling, thereby make the axial force and the lateral force that are calculated more accurate.

The specific embodiment that creeps into the Forecasting Methodology of friction torque and drill bit advancing direction according to coastal waters of the present invention horizontal well is described below.

As shown in Figure 2, Forecasting Methodology according to the present invention comprises the steps:

S1. import the design parameters of drilling well, comprise the drill string total length, full well well depth, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density etc.; Measure the well trajectory parameters, comprise well depth, hole angle, the azimuth of well track each point;

S2. form virtual drilling engineering actual condition; Utilize the well track parameter of the design parameters imported among the step S1 and measurement to form a virtual drilling process digital image; This image reproduces full well drill string, the borehole wall, the well curve shape in the actual well drilled process, the relative position of drilling rod, heavy weight drill pipe, drill collar and well truly;

S3. according to formula (1) drill string is divided into many tiny unit; Getting full well drill string is research object, and drill string can be considered elongated any space curve reinforcing beam in well, and its coordinate system is seen Fig. 1 (a);

S4. form the element stiffness matrix [k] of drill string, set up the unit equilibrium equation according to formula (2);

S5. form drill string integral rigidity matrix [K];

S6. { F} promptly obtains axial force, lateral force, moment of torsion and the moment of flexure etc. of each unit to calculate the whole joint forces vector of stressing conditions of node of each unit of expression according to formula (5);

S7. { Q}, wherein iterative process comprises the steps: to draw whole displacement of joint vector according to formula (5) and formula (6) by iteration

S71. determine the displacement φ of each node of drill string according to whole machine balancing equation (5) _i

S72. determine displacement φ _iGreater than borehole wall clearance delta _iNode;

S73. with the displacement assignment of this node with borehole wall clearance delta _iValue, even

φ _i＝Δ _i

S74. ask the displacement of other nodes of drill string again according to whole machine balancing equation (5), still have the displacement φ of some nodes this moment _iMay be greater than the clearance delta of the borehole wall _i, repeating step S71-S73 satisfies condition up to the displacement of all nodes | φ _i|≤Δ _iTill;

S75. after step S71 to S74, some contact point had become the noncontact point originally, will revise for this situation; The method of revising is, original all contact points are subjected to the judgement of force direction, when certain contact point be subjected to force direction to point to borehole wall direction by hole axis the time, determine that this point is real contact point; When certain contact point be subjected to force direction to point to hole axis by the borehole wall time, determine that this point is virtual connection contact (being the noncontact point), answer constraint relief, promptly make the displacement φ that the virtual connection contact is located _i＜Δ _i

S76. repeating step S71 to S75 meets borehole wall geometrical boundary condition up to the displacement of whole drill strings | φ _i|≤Δ _iTill, all real contact points of the definite thus drill string and the borehole wall after determining real contact point, not only can be determined the form of drill string in well, and can determine the size and the direction of each node lateral force of drill string;

S8. according to formula (8) and (9), utilize and find the solution the whole joint forces vector that (5) formula obtains { end value of F} is calculated the axial rub resistance and the friction torque of full well drill string;

S9. obtain the make a concerted effort π and at the make a concerted effort ω of aximuthpiston of drill bit according to formula (10) and (11) on the hole deviation plane;

S10. obtain the deflecting direction angle alpha in final drill bit future and the azimuthal angle beta in drill bit future according to formula (14) and (15), thereby obtain the direction that downhole drill bit will creep into;

Wherein k obtains by iteration according to formula (16).

The process of setting up drill string and well entity is such: the design parameters that utilizes the drilling well of input, comprise the drill string total length, full well well depth, borehole diameter, drill string internal diameter, the drill string external diameter, casing inner diameter, cover external diameter of pipe, the friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density; With measured well track parameter, comprise well depth, hole angle, the azimuth of well track each point, make drill string and well become the actual object that possesses the every physical parameter of three dimensions, be used to set up a virtual drill string form and a well track; Method for building up is for to input to computer with all parameters of having measured, computer dwindles above measured parameter by a certain percentage then, form the virtual image of a drill string and well with universal method, and carry out the simulation demonstration of digitlization storage and computer screen.For example, the universal method of above-mentioned formation drill string and well virtual image can be such method, above-mentioned parameter is inputed to softwares such as AUTO CAD, then the drill string that directly generates with this software and the virtual image of well.

Setting up the purpose of unit equilibrium equation, is that junior unit is set up equilibrium relation between the stressed and displacement, can obtain the suffered active force and the displacement of unit node with this.

Above-mentioned unit equilibrium equation is corresponding to the stress of some unit of drill string and the equilibrium relation between the displacement; With the stiffness matrix [k] of these unit method according to prior art, for example the stiffness matrix assemble method in the nonlinear finite element is assembled into whole nonlinear stiffness matrix [K].

According to the various boundary of well-drilling borehole, can be in above-mentioned whole machine balancing equation deterministic force { { one among the Q} is known quantity, and another is a unknown quantity for F} and displacement.For example, when drill bit creeps into, creep into the power of moment in order to try to achieve drill bit and since this moment the drill bit place axial displacement be zero, and axial force be the unknown simultaneously, so just can obtain the axial force of drill bit by following formula.Again for example, there are two nodes up and down a unit of drill string, power in the middle of drill string on the node of certain unit can be by the power of a unit and next unit on this unit, method by recursion is tried to achieve, but this moment, the displacement of drill string this element was a unknown quantity, can obtain the displacement of this unit by following formula.Finding the solution the power and the displacement of each unit of drill string by above-mentioned equilibrium equation, to those skilled in the art, is a kind of general knowledge.Finding the solution of above-mentioned equilibrium equation is not inventive point of the present invention, at this, no longer is described in greater detail.

Shown in Fig. 3 is block diagram according to the control method of drill bit advancing direction in the horizontal well drilling process of coastal waters of the present invention.As shown in Figure 3, be on the basis of the Forecasting Methodology of drill bit advancing direction in the horizontal well drilling process of coastal waters according to the present invention according to the control method of drill bit advancing direction in the horizontal well drilling process of coastal waters of the present invention, further comprise the steps:

S11. the data with the drilling direction in relevant drill bit future of prediction compare with original well track design data;

S12. will revise data input near-bit stabilizer according to comparative result;

S13. revise the actual drilling direction of drill bit, to ensure that drill bit creeps into by original planned course.

Shown in Fig. 4 is embodiment according to the control system of drill bit advancing direction in the horizontal well drilling process of coastal waters of the present invention.Describe this embodiment of the present invention in detail below with reference to Fig. 4.

As shown in Figure 4, this control system comprises a control device 100;

Well-drilling borehole trajectory measurement device 200 is used to measure the well-drilling borehole trajectory parameters, comprising well depth, hole angle, the azimuth of well track each point;

Design parameters input unit 300, be used for design parameters, comprise the drill string total length, full well well depth to control device 100 input drilling wells, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, the cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density etc.;

Signal receiving device 400 is used to receive the control signal of described control device, and control can change the control attitude of the near-bit stabilizer 500 of drill bit drilling direction;

Wherein, described control device 100 receives the well-drilling borehole trajectory parameters of well-drilling borehole trajectory measurement device 200 measurements and the design parameters of this drilling well that design parameters input unit 300 is imported, and forms a virtual drilling process digital image.This image reproduces full well drill string, the well curve shape in the actual well drilled process, the relative position of drilling rod, heavy weight drill pipe, drill collar and well truly.

Then, described control device 100 is carried out following operation:

According to formula (1) drill string is divided into many tiny unit;

Form the element stiffness matrix [k] of drill string, set up the unit equilibrium equation according to formula (2);

Form drill string integral rigidity matrix [K];

Calculate the whole joint forces vector of stressing conditions of node of each unit of expression { F} promptly obtains axial force, lateral force, moment of torsion and the moment of flexure etc. of each unit according to formula (5).

{ Q}, wherein iterative process comprises the steps: to draw whole displacement of joint vector according to formula (5) and formula (6) by iteration

S71. determine the displacement φ of each node of drill string according to whole machine balancing equation (5) _i

S72. determine displacement φ _iGreater than borehole wall clearance delta _iNode;

S73. with the displacement assignment of this node with borehole wall clearance delta _iValue, even

φ _i＝Δ _i

S74. ask the displacement of other nodes of drill string again according to whole machine balancing equation (5), repeating step S71-S73 satisfies condition up to the displacement of all nodes | φ _i|≤Δ _iTill;

S75. all contact points are subjected to the judgement of force direction, when certain contact point be subjected to force direction to point to borehole wall direction by hole axis the time, determine that this point is real contact point; When certain contact point be subjected to force direction to point to hole axis by the borehole wall time, determine that this point is the virtual connection contact, constraint relief promptly makes the displacement φ that the virtual connection contact is located _i＜Δ _i

S76. repeating step S71 to S75 meets borehole wall geometrical boundary condition up to the displacement of whole drill strings | φ _i|≤Δ _iTill, all real contact points of the definite thus drill string and the borehole wall.

According to formula (8) and (9), utilize and to find the solution the whole joint forces vector that (5) formula obtains { end value of F} is calculated the axial rub resistance and the friction torque of full well drill string;

Obtain the make a concerted effort π and at the make a concerted effort ω of aximuthpiston of drill bit according to formula (10) and (11) on the hole deviation plane;

Obtain the deflecting direction angle alpha in final drill bit future and the azimuthal angle beta in drill bit future according to formula (14) and (15), thereby obtain the direction that downhole drill bit will creep into;

Wherein k obtains by iteration according to formula (16).

Data and original well track design data about the drilling direction in drill bit future are compared, send instruction according to comparative result to signal receiving device, in order to revise the drill bit drilling direction, to ensure that drill bit creeps into by original planned course.

Introduce the application example that creeps into the Forecasting Methodology of frictional resistance and drill bit advancing direction according to coastal waters of the present invention horizontal well below.

The wellbore trajectory data of a well on the applied platform of the present invention see Table 1.Table 2 is listed be in this well drilling process the actual measurement moment of torsion, utilize the horizontal well torque parameter the resulting moment of torsion of linear prediction method the linear prediction result and utilize horizontal well according to the present invention to creep into nonlinear prediction result's the contrast situation of the resulting moment of torsion of nonlinear prediction method of frictional resistance.

Table 1

Sequence number	Tiltedly dark (m)	Hole deviation (deg)	Orientation (deg)	Key point
					1 2 3 4 5 6 7 8 9 10 11 12	1050.0 1150.0 1250.0 1346.0 2375.87 2425.87 2525.87 2611.81 2658.79 2704.64 2735.64 2758.64	1.00 10.0 20.0 29.6 29.6 41.73 53.78 65.58 82.92 91.49 91.49 91.49	1.00 259.18 259.18 259.18 259.19 259.19 259.19 259.85 259.27 259.64 259.64 259.63	Top base

Table 2

Sequence number	Depth measurement (m)	Nonlinear prediction moment of torsion (kNm)	Linear prediction moment of torsion (kNm)	Actual measurement friction torque (kNm)
					1 2 3 4 5 6 7 8 9 10 11 12 13	1600 1700 1800 1900 2050 2100 2200 2300 2400 2500 2600 2700 2758	6.05 8.27 8.45 1.66 12.94 12.76 8.58 8.07 13.63 11.01 0.28 0.29 0.38	10.05 10.27 10.45 10.66 10.81 10.94 11.76 12.58 13.07 14.01 14.28 14.29 14.38	10.84 13.55 14.91 8.13 7.68 10.16 7.45 10.16 10.84 13.55 12.88 11.52

The mode of Fig. 5 and 6 usefulness curves has been expressed the linear prediction moment of torsion and the comparable situation of actual measurement moment of torsion and the nonlinear prediction moment of torsion and actual measurement moment of torsion contrast situation of this well of this well respectively, wherein, the actual measurement moment of torsion of curve 1 this well of expression, the nonlinear prediction result of the moment of torsion of curve 2 these wells of expression, the linear prediction result of the moment of torsion of curve 3 these wells of expression.

From result of calculation, non-linear moment of torsion predicts that the trend of predicting than linear moment of torsion is more similar in appearance to actual drilling process.

From Fig. 5, non-linear moment of torsion predicts the outcome very approaching with the trend of actual drilling process, even several torque peak point all roughly coincide.This point for the generation degree of depth of estimating peak torque before horizontal well spuds in, is carried out the preparation that prevents bit freezing in advance, is equipped with the rig power of big power reserve coefficient, all is significant.

From Fig. 6, linear moment of torsion predicted value has reflected the average of actual torque in whole creeping into, and this is for the rotary power demand of pre-estimating rig, and the rough overall variation of creeping into middle moment of torsion of grasping is to can be used as a reference.Yet as if the torque peak point that will probe in detail in the drilling process, so linear torque caculation method is inaccessible absolutely.

Table 3 is listed is the predicted value and the measured value of drill bit drilling direction that utilizes this well of Forecasting Methodology gained morals of coastal waters of the present invention horizontal well drill bit advancing direction.

Table 3

Sequence number	Depth measurement (m)	Drill bit direction of deflection prediction (deg)	Drill bit azimuth direction prediction (deg)	Actual measurement drill bit direction
						Hole deviation	The orientation
				1 2 3 4 5 6 7 8 9 10 11 12 13	1600 1700 1800 1900 2050 2100 2200 2300 2400 2500 2600 2700 2758			3.43 drop angle 4.62 drop angles 4.62 drop angles 6.69 drop angles 4.24 drop angles 4.25 drop angles 3.46 drop angles 3.3 drop angles 0.09 drop angle 5.90 drop angles 1.34 drop angles 1.34 drop angles 1.77 drop angles	00 3.62 left sides are floated 3.62 left sides and are floated 2.51 left sides and float 0.36 right side and float 0.325 right side and float 0.14 right side and float 0.04 right side and float 0.048 left side and float 0.863 left side and float 000000	Drop angle drop angle drop angle drop angle increasing hole angle increasing hole angle drop angle drop angle drop angle	0 right side is floated the right side and is floated a left side and float a little left side and float a little left side and float a little left side and float a little left side and float a left side and float

Data from table 3 contrast as can be seen, and the predictablity rate of drill bit direction of deflection is 78.9%, and the predictablity rate of drill bit azimuth direction is 57.1%.So far still have nothing to do and move towards bibliographical information, so these characteristics not only there are important practice significance, also have than important significance for theories in prediction drill bit in the prediction frictional resistance.

Claims (12)

1. the Forecasting Methodology of a coastal waters horizontal well Drilling bore bit direction of advance may further comprise the steps:

The design parameters of input drilling well comprises the drill string total length, full well well depth, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density;

Measure the well trajectory parameters, comprise well depth, hole angle, the azimuth of well track each point;

Utilize the well track parameter of above-mentioned design parameters and measurement to form virtual drilling engineering actual condition;

Formed drill string is divided into a plurality of unit, and the two ends of this unit are node;

Determine the whole displacement of joint vector of whole joint forces vector sum of drill string and the real contact point of each node of definite drill string and the borehole wall according to nonlinear finite element method;

Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future.

2. the Forecasting Methodology of coastal waters according to claim 1 horizontal well Drilling bore bit direction of advance, it is characterized in that, determine the whole displacement of joint vector of whole joint forces vector sum of drill string and determine that the step of the real contact point of each node of drill string and the borehole wall comprises the steps:

Form the element stiffness matrix [k] of drill string, and according to formula

[k]{q}＝{f}

Set up the unit equilibrium equation, wherein, { q} is a unit displacement of joint vector; { f} is a unit joint forces vector;

Form drill string global stiffness matrix [K];

According to formula

[K]{Q}＝{F}

The whole joint forces vector of the stressing conditions of the node of each unit of calculating expression F}, wherein, { Q} is whole displacement of joint vector;

According to formula

[K]{Q}＝{F}

With | φ _i|≤Δ _i

By iteration draw whole displacement of joint vector Q}, wherein, φ _iDisplacement { Q for i node of drill string _iAt the displacement projection perpendicular to the borehole axis direction, { Q _iBe { the displacement summation of Q} displacement array on i node, Δ _iBe the drill string of i node of drill string and the displacement restriction amount between the borehole wall;

Butt contact is subjected to the judgement of force direction, determines all real contact points of the drill string and the borehole wall thus.

3. the Forecasting Methodology of coastal waters as claimed in claim 2 horizontal well drill bit advancing direction is characterized in that, { Q} also determines that the step of all real contact points of the drill string and the borehole wall comprises the steps: to described definite whole displacement of joint vector

({ Q}={F} determines the displacement φ of each node of drill string to 1} according to whole machine balancing equation [K] _i

(2) determine displacement φ _iGreater than borehole wall clearance delta _iNode;

(3) with the displacement assignment of determined node with borehole wall clearance delta _iValue, even

φ _i＝Δ _i

(4) repeating step (1) is asked the displacement of other nodes of drill string to (3), satisfies condition up to the displacement of all nodes | φ _i|≤Δ _iTill;

(5) all contact points are subjected to the judgement of force direction, when certain contact point be subjected to force direction to point to borehole wall direction by hole axis the time, determine that this point is real contact point; When certain contact point be subjected to force direction to point to hole axis by the borehole wall time, determine that this point is the virtual connection contact, constraint relief promptly makes the displacement φ that the virtual connection contact is located _i＜Δ _i

(6) repeating step (1) is to (5), meets borehole wall geometrical boundary condition up to the displacement of whole drill strings | φ _i|≤Δ _iTill, all real contact points of the definite thus drill string and the borehole wall.

4. as the Forecasting Methodology of any described coastal waters horizontal well drill bit advancing direction among the claim 1-3, it is characterized in that the step of the drilling direction in described definite drill bit future comprises the steps:

According to formula

R＝{μ} ^T·{F}

M＝μ·{r} ^T·{F}

Calculate the axial rub resistance R and the friction torque M of full well drill string, wherein, { μ } is the friction factor array between the drill string and the borehole wall; { r} is the practical function radius array of drill string and each contact point of the borehole wall;

According to formula

π＝τ+η

ω＝τ+ξ

Obtain the make a concerted effort π and at the make a concerted effort ω of aximuthpiston of drill bit on the hole deviation plane, wherein, τ is the axial force of shaft bottom drill bit, and η is the lateral force of the suffered direction of deflection of drill bit, and ξ is the lateral force of azimuth direction;

According to formula

$\mathrm{\α}=\mathrm{arctg}\frac{\mathrm{k\η}}{\mathrm{\τ}},\mathrm{\β}=\mathrm{arctg}\frac{\mathrm{k\ξ}}{\mathrm{\τ}}$

Obtain the deflecting direction angle alpha in final drill bit future and the azimuthal angle beta in drill bit future, thereby obtain the direction that downhole drill bit will creep into;

Wherein k is obtained by following formula iteration:

$\frac{\mathrm{\τ}}{\mathrm{\π}}=\ln \frac{1-\sqrt{1-k^2}}{k}+\sqrt{1-k^2}.$

5. the control method of a coastal waters horizontal well Drilling bore bit direction of advance may further comprise the steps:

The design parameters of input drilling well comprises the drill string total length, full well well depth, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density;

Measure the well trajectory parameters, comprise well depth, hole angle, the azimuth of well track each point;

Utilize the well track parameter of above-mentioned design parameters and measurement to form virtual drilling engineering actual condition;

Formed drill string is divided into a plurality of unit, and the two ends of this unit are node;

Determine the whole displacement of joint vector of whole joint forces vector sum of drill string and the real contact point of each node of definite drill string and the borehole wall according to nonlinear finite element method;

Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future;

Data and original well track design data about the drilling direction in drill bit future are compared, send instruction according to comparative result to near-bit stabilizer, in order to revise the drill bit drilling direction, to ensure that drill bit creeps into by original planned course.

6. the control method of coastal waters according to claim 5 horizontal well Drilling bore bit direction of advance, it is characterized in that, determine the whole displacement of joint vector of whole joint forces vector sum of drill string and determine that the step of the real contact point of each node of drill string and the borehole wall comprises the steps:

Form the element stiffness matrix [k] of drill string, and according to formula

[k]{q}＝{f}

Set up the unit equilibrium equation, wherein, { q} is a unit displacement of joint vector; { f} is a unit joint forces vector;

Form drill string global stiffness matrix [K];

According to formula

[K]{Q}＝{F}

The whole joint forces vector of the stressing conditions of the node of each unit of calculating expression F}, wherein, { Q} is whole displacement of joint vector;

According to formula

[K]{Q}＝{F}

With | φ _i|≤Δ _i

By iteration draw whole displacement of joint vector Q}, wherein, φ _iDisplacement { Q for i node of drill string _iAt the displacement projection perpendicular to the borehole axis direction, { Q _iBe { the displacement summation of Q} displacement array on i node, Δ _iBe the drill string of i node of drill string and the displacement restriction amount between the borehole wall;

Butt contact is subjected to the judgement of force direction, determines all real contact points of the drill string and the borehole wall thus.

7. the control method of coastal waters as claimed in claim 6 horizontal well drill bit advancing direction is characterized in that, { Q} also determines that the step of all real contact points of the drill string and the borehole wall comprises the steps: to described definite whole displacement of joint vector

(1) { Q}={F} determines the displacement φ of each node of drill string according to whole machine balancing equation [K] _i

(2) determine displacement φ _iGreater than borehole wall clearance delta _iNode;

(3) with the displacement assignment of determined node with borehole wall clearance delta _iValue, even

φ _i＝Δ _i

(4) repeating step (1) is asked the displacement of other nodes of drill string to (3), satisfies condition up to the displacement of all nodes | φ _i|≤Δ _iTill;

(5) all contact points are subjected to the judgement of force direction, when certain contact point be subjected to force direction to point to borehole wall direction by hole axis the time, determine that this point is real contact point; When certain contact point be subjected to force direction to point to hole axis by the borehole wall time, determine that this point is the virtual connection contact, constraint relief promptly makes the displacement φ that the virtual connection contact is located _i＜Δ _i

(6) repeating step (1) is to (5), meets borehole wall geometrical boundary condition up to the displacement of whole drill strings | φ _i|≤Δ _iTill, all real contact points of the definite thus drill string and the borehole wall.

8. as the control method of any described coastal waters horizontal well drill bit advancing direction among the claim 5-7, it is characterized in that the step of the drilling direction in described definite drill bit future comprises the steps:

According to formula

R＝{μ} ^T·{F}

M＝μ·{r} ^T·{F}

Calculate the axial rub resistance R and the friction torque M of full well drill string, wherein, { μ } is the friction factor array between the drill string and the borehole wall; { r} is the practical function radius array of drill string and each contact point of the borehole wall;

According to formula

π＝τ+η

ω＝τ+ξ

Obtain the make a concerted effort π and at the make a concerted effort ω of aximuthpiston of drill bit on the hole deviation plane, wherein, τ be the axial force of subdrilling head also, and η is the lateral force of the suffered direction of deflection of drill bit, and ξ is the lateral force of azimuth direction;

According to formula

$\mathrm{\α}=\mathrm{arctg}\frac{\mathrm{k\η}}{\mathrm{\τ}},\mathrm{\β}=\mathrm{arctg}\frac{\mathrm{k\ξ}}{\mathrm{\τ}}$

Obtain the deflecting direction angle alpha in final drill bit future and the azimuthal angle beta in drill bit future, thereby obtain the direction that downhole drill bit will creep into;

Wherein k is obtained by following formula iteration:

$\frac{\mathrm{\τ}}{\mathrm{\π}}=\ln \frac{1-\sqrt{1-k^2}}{k}+\sqrt{1-k^2}.$

9. the control system of a coastal waters horizontal well Drilling bore bit direction of advance comprises:

Control device (100);

Well-drilling borehole trajectory measurement device (200) is used to measure the well-drilling borehole trajectory parameters, comprising well depth, hole angle, the azimuth of well track each point;

Design parameters input unit (300), be used for design parameters, comprise the drill string total length, full well well depth to described control device (100) input drilling well, borehole diameter, the drill string internal diameter, drill string external diameter, casing inner diameter, the cover external diameter of pipe, friction factor array between the drill string and the borehole wall, the practical function radius of drill string and each contact point of the borehole wall, drilling fluid density;

Signal receiving device (400) is used to receive the control signal of described control device (100), and control can change the control attitude of the near-bit stabilizer (500) of drill bit drilling direction;

Wherein, described control device (100) receives the well-drilling borehole trajectory parameters of described well-drilling borehole trajectory measurement device (200) measurement and the design parameters of this drilling well that described design parameters input unit (300) is imported, and forms virtual drilling engineering actual condition; Formed drill string is divided into a plurality of unit, and the two ends of this unit are node; Determine the whole displacement of joint vector of whole joint forces vector sum of drill string according to nonlinear finite element method; Determine the real contact point of each node of drill string and the borehole wall; Axial force and lateral force according to the drill bit place are determined the drill bit drilling direction in future; Data and original well track design data about the drilling direction in drill bit future are compared, send instruction according to comparative result to signal receiving device, in order to revise the drill bit drilling direction, to ensure that drill bit creeps into by original planned course.

10. the control system of coastal waters according to claim 9 horizontal well Drilling bore bit direction of advance, it is characterized in that described control device is by implementing the real contact point that following steps are determined the whole displacement of joint vector of whole joint forces vector sum of drill string and determined each node of drill string and the borehole wall:

Form the element stiffness matrix [k] of drill string, and according to formula

[k]{q}＝{f}

Set up the unit equilibrium equation, wherein, { q} is a unit displacement of joint vector; { f} is a unit joint forces vector;

Form drill string global stiffness matrix [K];

According to formula

[K]{Q}＝{F}

The whole joint forces vector of the stressing conditions of the node of each unit of calculating expression F}, wherein, { Q} is whole displacement of joint vector;

According to formula

[K]{Q}＝{F}

With | φ _i|≤Δ _i

By iteration draw whole displacement of joint vector Q}, wherein, φ _iDisplacement { Q for i node of drill string _iAt the displacement projection perpendicular to the borehole axis direction, { Q _iBe { the displacement summation of Q} displacement array on i node, Δ _iBe the drill string of i node of drill string and the displacement restriction amount between the borehole wall;

Butt contact is subjected to the judgement of force direction, determines all real contact points of the drill string and the borehole wall thus.

11. the control system of coastal waters as claimed in claim 10 horizontal well drill bit advancing direction is characterized in that, described control device by implement following steps determine whole displacement of joint vector Q} also determines all real contact points of the drill string and the borehole wall:

(1) { Q}={F} determines the displacement φ of each node of drill string according to whole machine balancing equation [K] _i

(2) determine displacement φ _iGreater than borehole wall clearance delta _iNode;

(3) with the displacement assignment of determined node with borehole wall clearance delta _iValue, even

φ _i＝Δ _i

(4) repeating step (1) is asked the displacement of other nodes of drill string to (3), satisfies condition up to the displacement of all nodes | φ _i|≤Δ _iTill;

(5) all contact points are subjected to the judgement of force direction, when certain contact point be subjected to force direction to point to borehole wall direction by hole axis the time, determine that this point is real contact point; When certain contact point be subjected to force direction to point to hole axis by the borehole wall time, determine that this point is the virtual connection contact, constraint relief promptly makes the displacement φ that the virtual connection contact is located _i＜Δ _i

(6) repeating step (1) is to (5), meets borehole wall geometrical boundary condition up to the displacement of whole drill strings | φ _i|≤Δ _iTill, all real contact points of the definite thus drill string and the borehole wall.

12. the control appliance as any described coastal waters horizontal well drill bit advancing direction among the claim 9-11 is characterized in that, described control device is determined the drill bit drilling direction in future by implementing following steps:

According to formula

R＝{μ} ^T·{F}

M＝μ·{r} ^T·{F}

Calculate the axial rub resistance R and the friction torque M of full well drill string, wherein, { μ } is the friction factor array between the drill string and the borehole wall; { r} is the practical function radius array of drill string and each contact point of the borehole wall;

According to formula

π＝τ+η

ω＝τ+ξ

Obtain the make a concerted effort π and at the make a concerted effort ω of aximuthpiston of drill bit on the hole deviation plane, wherein, τ is the axial force of shaft bottom drill bit, and η is the lateral force of the suffered direction of deflection of drill bit, and ξ is the lateral force of azimuth direction;

According to formula

$\mathrm{\α}=\mathrm{arctg}\frac{\mathrm{k\η}}{\mathrm{\τ}},\mathrm{\β}=\mathrm{arctg}\frac{\mathrm{k\ξ}}{\mathrm{\τ}}$

Obtain the deflecting direction angle alpha in final drill bit future and the azimuthal angle beta in drill bit future, thereby obtain the direction that downhole drill bit will creep into;

Wherein k is obtained by following formula iteration:

$\frac{\mathrm{\τ}}{\mathrm{\π}}=\ln \frac{1-\sqrt{1-k^2}}{k}+\sqrt{1-k^2}.$

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