阅读说明：本技术 油气井水平段开泵的桥射联作泵送速度控制曲线计算方法 (Method for calculating bridge-injection combined pumping speed control curve of oil-gas well horizontal segment pump ) 是由 杨登波 陈锋 唐凯 任国辉 陈建波 罗苗壮 张清彬 刘勇军 李妍僖 聂靖雯 于 2020-04-14 设计创作，主要内容包括：本发明公开了油气井水平段开泵的桥射联作泵送速度控制曲线计算方法,计算泵送推力等于静摩擦力时泵送管串的泵送排量；计算泵送推力等于动摩擦力时,第一阶段排量对应的极限泵送速度；确定第一阶段排量作用下的泵送速度变化范围,取该范围中的任意速度值,计算达到该速度所需的加速时间；判断第一阶段排量对应的极限泵送速度是否达到水平段重复泵送所期望的速度范围,若达到,绘制曲线,若未达到,提升泵送管串的泵送排量并继续计算速度对应的加速时间,直至达到。本发明通过计算出各阶段排量下的速度及对应加速时间,描述不同排量下的泵送速度变化趋势,为油气井水平段重复泵送提供了一种可指导现场作业的速度控制曲线,为现场操作提供理论依据。(The invention discloses a method for calculating a bridge-shooting combined pumping speed control curve of a pump at a horizontal section of an oil-gas well, which is used for calculating the pumping displacement of a pumping pipe string when the pumping thrust is equal to the static friction; calculating the limit pumping speed corresponding to the first-stage displacement when the pumping thrust is equal to the dynamic friction force; determining the pumping speed variation range under the action of the first-stage displacement, taking any speed value in the range, and calculating the acceleration time required for reaching the speed; and judging whether the limit pumping speed corresponding to the first-stage displacement reaches the speed range expected by the repeated pumping of the horizontal stage, if so, drawing a curve, and if not, increasing the pumping displacement of the pumping pipe string and continuously calculating the acceleration time corresponding to the speed until the speed reaches. The invention describes the change trend of the pumping speed under different discharge capacities by calculating the speed and the corresponding acceleration time under each discharge capacity, provides a speed control curve capable of guiding field operation for repeated pumping of the horizontal section of the oil-gas well, and provides a theoretical basis for field operation.)

1. The method for calculating the control curve of the pumping speed of the bridge-shooting combined pumping at the horizontal section of the oil-gas well is characterized by comprising the following steps of:

step 1: calculating the pumping displacement of the pumping pipe string when the pumping thrust is equal to the static friction force according to the static friction force and the dynamic friction force of the horizontal-segment repeated pumping pipe string and the cable, wherein the pumping displacement at the moment is the critical displacement and is recorded as the first-stage displacement;

step 2: calculating the limit pumping speed corresponding to the first-stage displacement when the pumping thrust is equal to the dynamic friction force according to the first-stage displacement obtained in the step 1;

and step 3: determining a pumping speed variation range under the action of the first-stage displacement by taking 0 as an initial value and the limit pumping speed corresponding to the first-stage displacement as an end value, taking any speed value in the range, and calculating the acceleration time required for reaching the speed;

and 4, step 4: if the limit pumping speed corresponding to the first-stage displacement reaches the speed range expected by the repeated pumping of the horizontal stage, executing a step 10; otherwise, executing step 5;

and 5: the pumping displacement of the pumping pipe string is lifted, and the lifted pumping displacement is recorded as the displacement of a new stage;

step 6: calculating the limit pumping speed corresponding to the displacement of the new stage when the pumping thrust is equal to the dynamic friction force according to the displacement of the new stage obtained in the step 5;

and 7: determining the pumping speed variation range under the action of the displacement of the new stage by taking the limit pumping speed corresponding to the displacement of the previous stage as an initial value and the limit pumping speed corresponding to the displacement of the new stage as a final value, and calculating the acceleration time required for reaching the speed by taking any speed value in the range;

and 8: if the limit pumping speed corresponding to the displacement of the new stage reaches the speed range expected by the repeated pumping of the horizontal stage, executing the step 10; otherwise, executing step 9;

and step 9: repeatedly executing the step 5 to the step 8 until the limit pumping speed corresponding to the displacement of a certain stage reaches the speed range expected by the repeated pumping of the horizontal stage, and executing the step 10;

step 10: taking any speed value under the displacement of each stage as a vertical coordinate, and taking the accumulated acceleration time corresponding to the speed as a horizontal coordinate, and drawing a bridge-shooting combined pumping speed control curve of the horizontal-stage pump; the accumulated acceleration time is the accumulated time from the moment when the horizontal segment of the repeated pumping pipe string starts to start.

2. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 1, wherein in the step 1, the calculation formula for calculating the pumping displacement of the pipe string when the pumping thrust is equal to the static friction force is as follows:

in the formula: q_kIs the k stage displacement; f_PkIs Q_kA corresponding pumping thrust; f. of_sThe static friction force of the pumping pipe string and the cable is obtained; f_PkAnd Q_kSubscript k in the step (1) represents a stage serial number, the value range of k is 1,2 … n, and the value of k in the step (1) is 1; a. the_jIs a bridge beamThe axial pressure action areas of all parts of the connecting pipe string are numbered sequentially from top to bottom; n is the number of pipe sleeve gaps with different sizes formed by the bridge-shooting connection pipe string due to different outer diameters of all components; mu and rho are respectively the viscosity and density of the pumping fluid; q_kIs the k stage displacement; d_iThe diameter of each component of the pipe string; l_i、h_iThe length and the height of each pipe sleeve gap are respectively;_ithe eccentricity of the axis of the pipe sleeve when the pipe string is contacted with the wall of the pipe sleeve.

3. The method for calculating the bridge-shooting combined pumping speed control curve of the oil and gas well horizontal segment pump-on according to claim 1, wherein in the step 1, the static friction force and the dynamic friction force of the horizontal segment repeated pumping pipe string and the cable are calculated according to the total weight of the horizontal segment repeated pumping pipe string and the cable in well fluid and the horizontal segment well oblique angle of the position where the pumping pipe string and the cable are located.

4. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 2, wherein in the step 2, the calculation formula of the limit pumping speed corresponding to the first-stage displacement is as follows:

wherein: f_pk＝X_k·v²-Y_k·v+Z_k；

In the formula: k in all variable symbol subscripts represents a stage serial number, and k is 1 in the step 2; f. of_dThe dynamic friction force of the pumping pipe string and the cable is obtained; m is the total weight of the pumping pipe string and the horizontal section cable in well fluid, and D is the inner diameter of the sleeve; v is the pumping speed.

5. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 4, wherein in the step 3, the calculation formula of the acceleration time required for reaching any speed in the corresponding speed variation range under the action of the first-stage displacement is as follows:

when y is_k ²-4x_kz_kAt > 0:

when y is_k ²-4x_kz_kWhen < 0:

in the formula: c_k1And C_k2Is a constant solved according to boundary conditions, C_k1And C_k2K in the subscripts represents the orderSegment sequence number.

6. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 1, wherein in the step 5, the pumping displacement of the pumping pipe string is improved by 0.1m³/min～0.2m³/min。

7. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 5, wherein in the step 6, the limit pumping speed calculation formula corresponding to the displacement of the new stage is as follows:

wherein: f_pk＝X_k·v²-Y_k·v+Z_k；

8. The method for calculating the bridge-shooting combined pumping speed control curve of the oil-gas well horizontal segment pump opening according to claim 7, wherein in the step 7, the calculation formula of the acceleration time required for reaching any speed in the corresponding speed change range under the action of the displacement of the new stage is as follows:

when y is_k ²-4x_kz_kAt > 0:

when y is_k ²-4x_kz_kWhen < 0:

Technical Field

The invention belongs to the field of application of a cable pumping bridge plug and perforation combined operation technology of an oil-gas horizontal well, and particularly relates to a method for calculating a bridge-perforation combined operation pumping speed control curve of a horizontal section pump of an oil-gas well.

Background

The cable pumping bridge plug and perforation combined operation is called as cable pumping bridge ejection combined operation for short, and is characterized by that on the premise of that the shaft and stratum have communication channels of pore channel or crack, etc. by means of wellhead cable blowout preventer, the bridge plug and perforation pipe string are placed by means of dead weight to a certain well deflection depth (straight well section), and then matched with well-logging winch by means of fracturing pump truck and well-logging winch, according to pumping design program, the bridge plug seat seal can be implemented by means of thrust produced by fluid flowing through pipe string and casing pipe gap, and the bridge ejection combined pipe string can be pumped to target layer, after depth-checking and positioning, it can be communicated with underground selective-sending controller by means of ground control system, and the selective-sending ignition can be implemented, then the perforating gun string can be lifted up, and aligned with the designed perforation position, and the selective-sending ignition can be. The process is used as a main technology for the staged fracturing reformation of unconventional oil and gas storage, and is popularized and applied for nearly thousand well times in blocks such as shale gas of Changning-Wigner, Chongqing Fuling, Yunnan Zhaotong and the like, coal bed gas of Shanxi province, shale oil of Xinjiang province and the like.

The method is influenced by factors such as irregular well track, complex well bore, pump truck failure, unreasonable control of pumping capacity or logging winch speed (cable lowering speed) and the like, and the situations of pipe string pumping blockage, pumping failure and the like easily occur in the cable pumping bridge launching linkage, so that the pipe string needs to be strung to a straight well section for pumping again.

The method for pumping the bridge-shooting combined operation pipe string from the abnormal pumping stop position to the straight well section again is called a 'straight well section repeated pumping method' under the condition that the bridge-shooting combined operation is not successfully completed by the first pumping, the bridge-shooting combined operation is realized by pumping twice or multiple times, but the repeated pumping well section is longer, so that the operation time and the pumping liquid consumption are increased in multiples, and the economical efficiency and the timeliness of the development of the oil-gas horizontal well are seriously influenced. Therefore, a horizontal section repeated pumping method is provided, namely, a pipe string is lifted for a certain distance (100-150 m) from a horizontal section pumping abnormal stop position, a cable at the top of the pipe string is ensured to be in a stretching state, then a fracturing pump truck is started on the ground, pumping liquid is injected into a shaft at a certain discharge capacity, the pipe string is accelerated from rest to a certain speed at the horizontal section by means of flowing differential pressure thrust generated by the pumping liquid in a gap between a sleeve and the pipe string, so that the pipe string is smoothly pumped to a target position, and bridge-shooting combined operation is completed. The horizontal segment repeated pumping method has short repeated pumping distance, high operation time efficiency and low cost, and is primarily applied to the cable pumping bridge-shooting combined operation of the oil-gas horizontal well.

The repeated pumping process of the horizontal segment is variable acceleration motion, and can be divided into four stages: static stage, accelerated motion stage after starting tube string, stable motion stage, and deceleration stage. When the pumping displacement is small and the pumping thrust is not enough to overcome the static friction force, the pipe string and the cable are static; when the pumping displacement is continuously increased to enable the pumping thrust to be larger than the static friction, the pipe string and the cable start to move, the resistance is converted from the static friction into the dynamic friction, the resistance is reduced, the pipe string and the cable do variable acceleration motion, the pumping speed is gradually increased, the flow velocity of the gap flow between the pipe string and the sleeve is gradually reduced under the condition that the pumping displacement is not changed, the pumping thrust borne by the pipe string is reduced, the acceleration of the pipe string and the cable is gradually reduced, the speed reaches the maximum value under the corresponding displacement after the pipe string and the cable undergo a variable acceleration process that the acceleration is gradually reduced from a certain value to zero, a relatively stable uniform motion stage is entered, and the power and the resistance of the pipe string are balanced; however, the uniform motion of the power and the resistance of the pipe string reaching the balance cannot be maintained, because the cable entering the horizontal section is continuously increased along with the pumping, the friction resistance is increased, the balance state that the power is equal to the resistance is broken, and the resistance is larger than the power, so that the pipe string and the cable do deceleration motion.

The key of the repeated pumping of the horizontal section is to control the lowering speed of the cable of the logging winch to be matched with the movement speed of the underground pipe string. The pumping displacement at different stages corresponds to different variable acceleration motions, so that the lowering speed of a cable of the logging winch is difficult to control to match the variable speed motion of the underground pipe string in the field application process of the process. At present, how to design the stage discharge capacity of the horizontal section for repeated pumping and how to control the pumping speed does not form a corresponding technical theory, the field operation completely depends on the on-site reaction of operators, and the operation success rate is low and the safety and reliability are poor.

Disclosure of Invention

Aiming at the technical problems in the prior art, the invention provides a method for calculating a bridge-shooting combined pumping speed control curve of a horizontal pump at an oil-gas well section, which provides theoretical basis and visual reference for field operation and improves the safety and reliability of field application of the technology.

In order to solve the technical problems, the invention is realized by the following technical scheme:

the method for calculating the control curve of the pumping speed of the bridge-shooting combined pumping of the horizontal section of the oil-gas well comprises the following steps:

step 1: calculating the pumping displacement of the pumping pipe string when the pumping thrust is equal to the static friction force according to the static friction force and the dynamic friction force of the horizontal-segment repeated pumping pipe string and the cable, wherein the pumping displacement at the moment is the critical displacement and is recorded as the first-stage displacement;

step 2: calculating the limit pumping speed corresponding to the first-stage displacement when the pumping thrust is equal to the dynamic friction force according to the first-stage displacement obtained in the step 1;

and step 3: determining a pumping speed variation range under the action of the first-stage displacement by taking 0 as an initial value and the limit pumping speed corresponding to the first-stage displacement as an end value, taking any speed value in the range, and calculating the acceleration time required for reaching the speed;

and 4, step 4: if the limit pumping speed corresponding to the first-stage displacement reaches the speed range expected by the repeated pumping of the horizontal stage, executing a step 10; otherwise, executing step 5;

and 5: the pumping displacement of the pumping pipe string is lifted, and the lifted pumping displacement is recorded as the displacement of a new stage;

step 6: calculating the limit pumping speed corresponding to the displacement of the new stage when the pumping thrust is equal to the dynamic friction force according to the displacement of the new stage obtained in the step 5;

and 7: determining the pumping speed variation range under the action of the displacement of the new stage by taking the limit pumping speed corresponding to the displacement of the previous stage as an initial value and the limit pumping speed corresponding to the displacement of the new stage as a final value, and calculating the acceleration time required for reaching the speed by taking any speed value in the range;

and 8: if the limit pumping speed corresponding to the displacement of the new stage reaches the speed range expected by the repeated pumping of the horizontal stage, executing the step 10; otherwise, executing step 9;

and step 9: repeatedly executing the step 5 to the step 8 until the limit pumping speed corresponding to the displacement of a certain stage reaches the speed range expected by the repeated pumping of the horizontal stage, and executing the step 10;

step 10: taking any speed value under the displacement of each stage as a vertical coordinate, and taking the accumulated acceleration time corresponding to the speed as a horizontal coordinate, and drawing a bridge-shooting combined pumping speed control curve of the horizontal-stage pump; the accumulated acceleration time is the accumulated time from the moment when the horizontal segment of the repeated pumping pipe string starts to start.

Further, in step 1, the formula for calculating the pumping displacement of the pipe string when the pumping thrust is equal to the static friction force is as follows:

in the formula: q_kIs the k stage displacement; f_PkIs Q_kA corresponding pumping thrust; f. of_sThe static friction force of the pumping pipe string and the cable is obtained; f_PkAnd Q_kSubscript k in the step (1) represents a stage serial number, the value range of k is 1,2 … n, and the value of k in the step (1) is 1; a. the_jThe axial pressure action areas of all parts are numbered sequentially from top to bottom for the bridge-shooting linkage pipe string; n is the number of pipe sleeve gaps with different sizes formed by the bridge-shooting connection pipe string due to different outer diameters of all components; mu and rho are respectively the viscosity and density of the pumping fluid; q_kIs the k stage displacement; d_iThe diameter of each component of the pipe string; l_i、h_iThe length and the height of each pipe sleeve gap are respectively;_ithe eccentricity of the axis of the pipe sleeve when the pipe string is contacted with the wall of the pipe sleeve.

Further, in the step 1, the static friction force and the dynamic friction force of the horizontal segment of the repeated pumping pipe string and the cable are calculated according to the total weight of the horizontal segment of the repeated pumping pipe string and the cable in the well fluid and the horizontal segment well inclination angle of the position of the pumping pipe string and the cable.

Further, in step 2, the formula of the limit pumping speed corresponding to the first-stage displacement is as follows:

wherein: f_pk＝X_k·v²-Y_k·v+Z_k；

In the formula: k in all variable symbol subscripts represents a stage serial number, and k is 1 in the step 2; f. of_dThe dynamic friction force of the pumping pipe string and the cable is obtained; m is the total weight of the pumping pipe string and the horizontal section cable in well fluid, and D is the inner diameter of the sleeve; v is the pumping speed.

Further, in step 3, the calculation formula of the acceleration time required to reach any speed within the corresponding speed variation range under the action of the displacement of the first stage is as follows:

when y is_k ²-4x_kz_kAt > 0:

when y is_k ²-4x_kz_kWhen < 0:

in the formula: c_k1And C_k2To solve according to boundary conditions to obtainConstant of (C)_k1And C_k2K in the subscript represents the stage number.

Further, in the step 5, the pumping displacement of the pumping pipe string is increased by 0.1m³/min～0.2m³/min。

Further, in step 6, the limit pumping speed corresponding to the new-stage displacement is calculated by the formula:

wherein: f_pk＝X_k·v²-Y_k·v+Z_k；

Further, in step 7, the calculation formula of the acceleration time required to reach any speed within the corresponding speed variation range under the action of the displacement of the new stage is as follows:

when y is_k ²-4x_kz_kAt > 0:

when y is_k ²-4x_kz_kWhen < 0:

compared with the prior art, the invention has at least the following beneficial effects: aiming at the current situations that a horizontal segment repeated pumping method has no technical theory support, the pumping speed change process corresponding to the stage discharge capacity is not clearly known, and the field operability and the safety reliability are poor, the bridge-shooting combined pumping speed control curve calculation method for the horizontal segment pumping of the oil-gas well provided by the invention describes the pumping speed change trend under different discharge capacities by calculating the speed and the corresponding acceleration time under each stage discharge capacity, provides a speed control curve capable of guiding the field operation for the horizontal segment repeated pumping of the oil-gas well, provides a theoretical basis and an intuitive reference for the field operation, and improves the safety reliability of the field application of the horizontal segment repeated pumping technology.

In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a schematic diagram of a bridge-injection linkage pipe string with a horizontal pump section;

FIG. 2 is a control curve of the pumping speed of the bridge-shooting combined operation with the pump opened at the horizontal section;

wherein: 1. a sleeve; 2. fishing spears and magnetic positioning; 3. a weight bar; 4. perforating gun strings; 5. and (4) a bridge plug.

Detailed Description

To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

The method for calculating the bridge-injection combined pumping speed control curve of the horizontal section pump-on of the oil-gas well is explained in detail as follows:

a. calculating static friction force and dynamic friction force of the horizontal-section repeated pumping pipe string and the cable according to the total weight of the horizontal-section repeated pumping pipe string and the cable in well fluid and the horizontal-section well inclination angle of the cable, and then calculating critical displacement when the pumping thrust is equal to the static friction force according to a pumping thrust calculation formula, wherein the critical displacement is the displacement which just can enable the pumping pipe string and the cable to start moving and is also called as stage 1 displacement (first-stage displacement);

b. solving an exact relational expression between pumping thrust and pumping speed according to the critical displacement, combining pumping resistance (namely, kinetic friction force) to give an exact relational expression between acceleration and pumping speed under the condition of the critical displacement, and then calculating stage limit pumping speed when the pumping thrust is equal to the kinetic friction force (namely, the acceleration is 0), wherein the stage limit pumping speed is the maximum motion speed which can be reached by the pipe string and the cable under the critical displacement;

c. converting to obtain an expression of the acceleration time required by any speed according to the exact relation between the acceleration and the pumping speed, then selecting any speed value between 0 and critical displacement stage limit pumping speeds (the limit pumping speed corresponding to the first stage displacement), and solving the acceleration time required for reaching the speed, wherein the more calculation points are selected, the more accurate the control curve of the pumping speed of the stage is depicted;

d. if the limit pumping speed corresponding to the displacement of the stage 1 reaches the speed range expected by the repeated pumping of the horizontal section, executing a step j; if the limit pumping speed corresponding to the displacement of the stage 1 does not reach the speed range expected by the repeated pumping of the horizontal section, executing a step e;

e. the discharge capacity is improved by 0.1m³/min～0.2m³Min to obtain new stage discharge capacity, preferably 0.2m of each time of lifting³/min；

f. E, according to the displacement of the new stage in the step e, calculating the limit pumping speed corresponding to the displacement of the new stage when the pumping thrust is equal to the dynamic friction force;

g. determining the pumping speed variation range under the action of the displacement of the new stage by taking the limit pumping speed corresponding to the displacement of the previous stage as the starting point and the limit pumping speed corresponding to the displacement of the new stage as the ending point, and calculating the acceleration time required for reaching the speed by taking any speed value in the range;

h. determine if the limit pumping speed for the new stage displacement reaches the speed range desired for the level segment repeat pumping? If yes, executing step j; if not, executing the step i;

i. repeating the steps e to h, and executing the step j until the limit pumping speed corresponding to the displacement of a certain stage reaches the speed range expected by the repeated pumping of the horizontal stage;

j. and drawing a bridge-shooting joint pumping speed control curve of the horizontal segment pump to guide field operation by taking any speed value under the displacement of each stage as a vertical coordinate and taking the accumulated acceleration time corresponding to the speed (namely accumulated from the starting moment of the horizontal segment repeated pumping pipe string) as a horizontal coordinate.

Specifically, in step a, the pumping thrust F_PkThe following expression is given:

remarking: f_PkAnd Δ P_kiIn the subscripts k representsThe phase number, k, ranges from 1,2 … n.

In formula (1): a. the_jThe axial pressure action areas of all parts are numbered sequentially from top to bottom of the bridge-shooting linkage pipe string; delta P_kiUnder the action of the displacement of the stage k, sequentially numbering fluid from top to bottom of the bridge-jet connection operation pipe string to flow through gaps between each pipe string and a sleeve (pipe sleeve gaps for short) to generate pressure drop; k is a radical of_iIs formed by A_jThe coefficient of composition is proved by derivationn is the number of pipe sleeve gaps with different sizes formed by the bridge-shooting connection pipe string due to different outer diameters of all components.

The bridge shooting connection pipe string has different outer diameters and lengths of all parts, pipe sleeve gaps with different sizes are formed between the bridge shooting connection pipe string and the sleeves, and the pressure drop generated when pumped liquid flows through the pipe sleeve gaps is as follows:

in formula (2): μ, ρ are the pumping hydrodynamic viscosity and density, respectively; q_kIs the pumping displacement of stage k; d is the inner diameter of the sleeve; v is the pumping speed; d_iThe diameter of each component of the pipe string; l_i、h_iThe length and the height of each pipe sleeve gap are respectively;_ithe eccentricity of the axis of the pipe sleeve when the pipe string is contacted with the wall of the pipe sleeve.

Equation (2) can be transformed into:

ΔP_ki＝a_i·v²-b_ki·v+c_ki(3)

wherein:

substituting formula (3) for formula (1) to obtain the relationship between pumping thrust and pumping speed:

F_Pk＝X_k·ν²-Y_k·ν+Z_k(7)

wherein:

remarking: the above formula is a general expression, k in the subscript of the variable symbol represents the stage number, the value range of k is 1,2 … n, and in step a, k takes a value of 1.

Critical displacement Q just before the string and cable start to move (string and cable speed 0)₁Generated pumping thrust F_P1Equal to the static friction force f of the pipe string and the cable_sThe three have the following relations:

in equation (11), the pumping thrust F of critical displacement_P1(static friction force f of pipe string and Cable_s) Is about Q₁Solving the equation to obtain the critical displacement Q of repeated pumping starting₁。

In step b, the critical displacement obtained in step a, namely the stage 1 displacement Q₁And (3) substituting the expressions (5) to (6) and combining the expressions (4), (8), (9) and (10) to obtain the exact relational expression between the pumping thrust and the pumping speed under the displacement condition of the stage 1.

The motion resistance of the pipe string and the cable after starting is the dynamic friction force f_dCritical displacementAcceleration a of a string under conditions_kThe following relationship exists with the pumping speed v:

in formula (12): m is the total weight of the pipe string and the horizontal section cable in the well fluid;

remarking: formula (12) is a general expression, and in step b, k in the variable symbol subscript is 1.

When the acceleration a is 0, the pumping speed reaches the limit speed v under the stage displacement_kmaxNamely, the following steps are provided:

x_k·v_kmax ²-y_k·v_kmax+z_k＝0 (13)

solving equation x according to equation (13)₁·v_1max ²-y₁·v_1max+z₁The limit pumping speed v under the displacement of the stage 1 can be obtained when the displacement is 0_1max。

In step c, due to the acceleration a_kEqual to the derivative of the velocity v with respect to the time t, which can be obtained from equation (12):

the relationship between any speed and corresponding acceleration time can be obtained according to equation (14):

① when y_k ²-4x_kz_kAt > 0:

② when y_k ²-4x_kz_kWhen < 0:

constants C in formulas (15) and (16)_k1、C_k2And solving according to the boundary condition (namely the acceleration time corresponding to the speed of the starting point of each phase is 0).

The time t required for acceleration from the initial speed of each stage to a specific speed v can be determined from the equation (15) or the equation (16).

In step d, if the displacement of the stage 1 corresponds to the limit pumping speed v_1maxWhen the speed range which is expected by the repeated pumping of the horizontal segment is reached, executing the step j; limiting pumping speed v corresponding to the displacement of the stage 1_1maxIf the speed range expected by the repeated pumping of the horizontal section is not reached, executing the step e;

in step e, the discharge capacity is increased by 0.2m³Min, obtaining the discharge capacity of a new stage;

in step F, according to the new-stage displacement in step e, referring to expressions (4) to (10) in step a, firstly establishing an expression F between pumping thrust and speed_Pk＝X_k·ν²-Y_k·ν+Z_kThen, a relation between the acceleration and the pumping speed is established with reference to equation (12) in step bLet a_kSolving the limit pumping speed v corresponding to the displacement of the new stage as 0_kmax；

Step g, determining a pumping speed variation range under the action of the displacement of the new stage by taking the limit pumping speed corresponding to the displacement of the previous stage as a start and the limit pumping speed corresponding to the displacement of the new stage as an end, determining a relational expression of the speed and the corresponding acceleration time by referring to the method in the step c, taking any speed value in the speed variation range, and calculating the acceleration time required for reaching the speed, wherein the more calculation points are selected, the more accurate the control curve of the pumping speed of the stage is depicted;

in step h, determine whether the limit pumping speed corresponding to the new stage displacement reaches the speed range expected for the horizontal stage repeated pumping? If yes, executing step j; if not, executing the step i;

in the step i, repeating the steps e-h until the limit pumping speed corresponding to the displacement of a certain stage reaches the speed range expected by the repeated pumping of the horizontal stage, and executing the step j;

in step j, an arbitrary speed value under the displacement of each stage is taken as a vertical coordinate, and the accumulated acceleration time corresponding to the speed (namely, accumulated from the moment when the horizontal segment repeated pumping pipe string starts to start) is taken as a horizontal coordinate, so that a bridge-shooting joint pumping speed control curve of the horizontal segment pump is drawn to guide the actual field operation.

The present invention is further explained by the above embodiments of the present invention with reference to a specific example.

Referring to fig. 1 to 2, a method for calculating a bridge-shooting combined pumping speed control curve of a pump at a horizontal section of an oil and gas well, as shown in fig. 1, relates to a casing and a pipe string structure comprising a casing 1, a fishing spear and a magnetic stator 2, a weighting rod 3, a perforating gun 4 and a bridge plug 5.

A method for calculating a bridge-shooting combined pumping speed control curve of a horizontal segment pump of an oil-gas well comprises the following steps:

step 1, calculating static friction force and dynamic friction force of the horizontal segment repeated pumping pipe string and the cable according to the weight of the horizontal segment repeated pumping pipe string and the cable in well fluid and the horizontal segment well inclination angle. Taking repeated pumping at a horizontal section of a well as an example, the pipe string structure is shown in figure 1 and comprises a casing pipe 1, a fishing spear and magnetic positioning 2, a weighting rod 3, a perforating gun string 4 and a bridge plug 5. The inner diameter D of the sleeve 1 is 0.1143m, the fishing spear and the outer diameter D of the magnetic positioning 2₁0.073m, length l₁0.8 m; outer diameter d of weight rod 3₂0.097m, length l₂3.2 m; outer diameter d of perforating gun string 4₃0.089m, length l₃3.37 m; outer diameter d of the bridge plug 5₄0.097m, length l₄The height of the clearance between each part of the pumping pipe string and the sleeve pipe is as follows in sequence: h is₁＝0.02065m、h₂＝0.00865m、h₃＝0.01265m、h₄0.00865 m; the eccentricity of the pipe sleeve axis when each part of the pumping pipe string is contacted with the pipe sleeve wall is as follows in sequence:₁＝0.4189、₂＝1、₃＝0.6838、₄1. The well is repeatedly pumped by a pump at a position 1500m of a horizontal section, the well inclination angle of the horizontal section is 92 degrees, the self weight of a bridge-injection combined pipe string and a cable in well liquid is 715kg, the well temperature is 135 ℃, the bottom hole pressure is 90MPa, the pumping hydrodynamic viscosity mu is 0.00023Pa s, and the pumping liquid density rho is 1000kg/m³. Calculating to obtain the static friction force f of the pipe string and the cable_s1992.4N (coefficient of static friction 0.25), kinetic friction force f_d1642.74N (the coefficient of dynamic friction is 0.2), and the number N of pipe sleeve gaps with different sizes formed by the bridge-injection connecting pipe string due to different outer diameters of all components is 4, then the critical displacement (stage 1 displacement) Q of repeated pumping starting is obtained through the formula (11)₁＝1.41485m³/min。

Step 2, critical displacement (stage 1 displacement) Q₁＝1.41485m³The formula (5) to (6) is substituted by/min, and the exact relation between the pumping thrust and the pumping speed is obtained by combining the formula (4) and the formulas (8) to (10): f_P1＝491.92v²1979.37v +1992.4, the pumping resistance, i.e. the kinetic friction, the acceleration at critical displacement is related to the pumping speed by the formula: a is₁＝0.688v²2.7683v +0.489, solution 0.688v²The ultimate pumping speed v at stage 1 displacement can be obtained from-2.7683 v +0.489 ═ 0_1max＝666.6m/h。

Step 3, due to a₁＝0.688v²-2.7683v +0.489, the acceleration time calculation is selected as equation (15), and the constant term C in equation (15) is calculated from the boundary condition (when t is 0, the velocity v is 0)₁When the acceleration time is-1.206, the acceleration time calculation expression is:wherein x is 0.688, y is 2.768, and z is 0.489. Respectively select 0 to v_1maxThe speed values between 100m/h, 200m/h, 300m/h, 400m/h, 500m/h, 550m/h, 570m/h, 590m/h, 600m/h, 610m/h, 620m/h, 630m/h, 640m/h, 650m/h, 660m/h, 665m/h and 666.6m/h are solved, and the required acceleration time corresponding to the speeds is as follows in sequence: 0.062s, 0.136s, 0.229s, 0.353s, 0.537s, 0.677s, 0.752s, 0.843s、0.899s、0.963s、1.04s、1.136s、1.262s、1.449s、1.815s、2.373s、3.967s。

Step 4, as the general pumping speed range is 2500-3000 m/h, the limit pumping speed v of the critical displacement stage of repeated pumping starting_1maxIf 666.6m/h does not reach the desired value, the pumping displacement is increased to the stage 2 displacement Q₂＝1.6m³Min, then calculating the discharge capacity Q of the stage 2 according to the formulas (4) to (10)₂The relationship between pumping thrust and pumping speed under the conditions is: f_P2＝491.92v²-2238.06v + 2547.23; the relation between the acceleration and the pumping speed is solved according to the formula (12) as follows: a is₂＝0.688v²-3.1302v+1.265。

Step 5, according to equation 0.688v²Solving for-3.1302 v + 1.265-0 yields the limit pumping speed v at stage 2 displacement_2max1613.9 m/h. Since the relationship between acceleration and pumping speed under stage 2 displacement conditions is: a is₂＝0.688v²-3.1302v +1.265, the acceleration time calculation is selected as equation (15), and the constant term C in equation (15) is calculated based on the boundary condition (when the phase t is 0, the velocity v is 666.6m/h)₁-1.074, the acceleration time calculation expression is:wherein x is 0.688, y is 3.1302, and z is 1.265. Respectively select v_1max～v_2maxThe speed values of the interval between two adjacent speed values are 800m/h, 900m/h, 1000m/h, 1100m/h, 1200m/h, 1300m/h, 1400m/h, 1500m/h, 1550m/h, 1570m/h, 1590m/h, 1600m/h, 1610m/h, 1611m/h, 1612m/h, 1613m/h and 1613.9m/h, and the required acceleration time corresponding to the speeds is solved as follows: 0.057s, 0.106s, 0.163s, 0.231s, 0.314s, 0.421s, 0.571s, 0.818s, 1.047s, 1.196s, 1.437s, 1.651s, 2.154s, 2.271s, 2.436s, 2.725s, 4.003 s.

Step 6, limiting pumping speed v under the displacement of the stage 2_2maxWhen 1613.9m/h has not yet reached the desired value, the pump displacement is increased to stage 3 displacement Q₃＝1.8m³Min, then calculating the discharge capacity Q of the stage 3 according to the formulas (4) to (10)₃The relationship between pumping thrust and pumping speed under the conditions is: f_P3＝491.92v²-2517.51v + 3223.03; the relation between the acceleration and the pumping speed is solved according to the formula (12) as follows: a is₃＝0.688v²-3.521v + 2.2102. Then according to equation 0.688v²Solving for-3.521 v + 2.2102-0 yields the limit pumping speed v at stage 3 displacement_3max2637.3 m/h. Since the relationship between acceleration and pumping speed under stage 3 displacement conditions is: a is₃＝0.688v²-3.521v +2.2102, the acceleration time calculation selects equation (15), and the constant term C in equation (15) is calculated based on the boundary condition (when t is 0, the velocity v is 1613.9m/h)₁When the acceleration time is-1.046, the acceleration time calculation expression is:wherein x is 0.688, y is 3.521, and z is 2.2102. Respectively select v_2max～v_3maxThe speed values between 1800m/h, 1900m/h, 2000m/h, 2100m/h, 2200m/h, 2300m/h, 2400m/h, 2500m/h, 2550m/h, 2570m/h, 2590m/h, 2600m/h, 2610m/h, 2620m/h, 2630m/h, 2635m/h, 2636m/h, 2637m/h and 2637.3m/h are solved, and the required acceleration time corresponding to the speeds is sequentially as follows: 0.075s, 0.122s, 0.177s, 0.243s, 0.322s, 0.422s, 0.559s, 0.774s, 0.952s, 1.055s, 1.195s, 1.289s, 1.413s, 1.594s, 1.936s, 2.393s, 2.617s, 3.180s, 4.253 s.

Step 7, limit pumping speed v due to stage 3 displacement_3maxThe delivery capacity does not need to be increased any more because 2637.3m/h is in the range of 2500-3000 m/h. The speed under the displacement of each stage is used as the ordinate, the accumulated acceleration time corresponding to each speed value (i.e. accumulated from the moment when the horizontal segment repeated pumping pipe string starts to start) is used as the abscissa, a curve is drawn, a bridge-shooting combined pumping speed control curve of the horizontal segment pump as shown in figure 2 is drawn immediately, and the site operation can design the displacement (Q) according to each stage₁～Q₃) Limit pumping speed (v) corresponding to the displacement of each stage_1max～v_3max) And the pumping speed variation trend reflected in figure 2 controls the repeated pumping process of the horizontal segment.

Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.