CN112459747A - Control method of pressure-limiting and regulating valve for pressure-controlled drilling based on cubic spline curve - Google Patents
Control method of pressure-limiting and regulating valve for pressure-controlled drilling based on cubic spline curve Download PDFInfo
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- 238000005553 drilling Methods 0.000 title claims abstract description 74
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- 239000007791 liquid phase Substances 0.000 claims description 15
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- E21B34/00—Valve arrangements for boreholes or wells
- E21B34/02—Valve arrangements for boreholes or wells in well heads
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- E—FIXED CONSTRUCTIONS
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- E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
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Abstract
The invention relates to the technical field of control methods for pressure-limiting and regulating valves of pressure-limiting and regulating wells, in particular to a control method for pressure-limiting and regulating valves of pressure-limiting and regulating wells based on cubic spline curves. After the control method disclosed by the invention is used for controlling the opening of the throttle valve, the effect of limiting the back pressure fluctuation can be achieved, the back pressure control of the pressure control drilling wellhead is stable, the problems of overflow and well leakage of a narrow density window possibly caused by the overshoot of the throttle valve can be avoided, the drilling complexity is reduced, and the pressure control of a shaft is more refined.
Description
Technical Field
The invention relates to the technical field of control methods of pressure limiting and regulating valves of pressure-controlled drilling, in particular to a control method of a pressure limiting and regulating valve of pressure-controlled drilling based on a cubic spline curve.
Background
Along with exploration and development of exploratory wells and ultra-deep wells, the condition of extremely narrow density windows in the drilling process frequently occurs, the problem of drilling the wells in the deep wells and the ultra-deep wells through the narrow density windows is well solved through the pressure-controlled drilling technology, however, the problem of overshoot of a throttle valve at the wellhead of the pressure-controlled drilling is the key problem of stable pressure control, at present, the pressure control at home and abroad is only limited to steady-state back pressure, the problem of water hammer caused by back pressure overshoot is not considered, and particularly, the problem of overshoot of gas-liquid flow and throttle valves in the gas overflow process is not in the way of people.
The regulation of the well mouth throttle valve for the pressure-controlled drilling is a key technology for providing underbalance and pressure-controlled drilling back pressure control, and the requirement of pressure limitation in the process of regulating the well mouth target back pressure is met by combining the well mouth target back pressure, so that the safe drilling of an oil-gas well is guaranteed. At present, the throttle valve is adjusted only by focusing on a target back pressure value, the problem of back pressure overshoot in the throttle valve adjusting process is not considered, and the overshooting back pressure causes shaft water hammer pressure, so that the problems of overflow and well leakage of a narrow density window are caused.
Disclosure of Invention
The invention provides a control method of a pressure-limiting and regulating valve for pressure-controlled drilling based on a cubic spline curve, overcomes the defects of the prior art, and can effectively solve the problem of back pressure overshoot in the regulating process of the existing throttle valve.
The technical scheme of the invention is realized by the following measures: a control method of pressure-control drilling pressure-limiting regulation valve based on cubic spline curve includes adjusting opening degree of a throttle valve to control wellhead back pressure when gas-liquid two-phase flow flows through a pressure-control drilling wellhead throttle valve, calculating opening degree of the throttle valve by utilizing limited wellhead back pressure in combination with a wellbore multiphase flow model, a wellbore multiphase water hammer pressure model, a multiphase water hammer transient pressure model and a multiphase water hammer pressure inversion throttle opening degree model before or during adjustment of the opening degree of the throttle valve, fitting the opening degree of the throttle valve through cubic spline fitting the opening degree of the throttle valve model to obtain a throttle valve action curve, and adjusting the opening degree of the throttle valve according to the throttle valve action curve.
The following is further optimization or/and improvement of the technical scheme of the invention:
the throttle opening value and the throttle action curve are obtained according to the following method:
the oil-gas-drilling fluid three-phase fluid continuous equation is as follows:
in the formula (1), A is the annular cross-sectional area, rhokIs the density of the oil phase, the gas phase and the drilling liquid phase, phikVolume fractions of oil phase, gas phase and drilling liquid phase, vkIs the oil/gas/drilling fluid phase velocity, k is the oil phase gas phase and the drilling fluid phase, t is the time, s is the annulus length,
the oil-gas-drilling fluid three-phase fluid momentum conservation is as follows:
in the formula (2), g is gravity acceleration; p is a radical offIn order to obtain the friction gradient, the friction gradient is adopted,
dispersing the annulus into N grids, and solving the grids one by one along the well bottom to the well head, wherein the continuous equation differential format of the drilling fluid is as follows:
the spillover oil continuity equation difference format is as follows:
considering gas phase solubility, the overflow gas phase continuous equation difference format is as follows:
the difference format of the conservation of momentum equation is as follows:
in the formula (6), the first and second groups,
in the formula (9), vsm、vso、vsgSlip velocity, rho, of drilling fluid, formation oil and formation gas, respectivelym、ρo、ρgDensity of drilling fluid, formation oil and formation gas respectively;
taking an annular infinitesimal section as a control body, wherein the motion equation is as follows:
in the formula (10), p is pressure (back pressure), g is gravity acceleration, s is well length along the annulus, theta is the included angle between the annulus and the horizontal plane, and tauoIs the friction stress of the drilling fluid to the annular hollow wall, X is the control body wet circumference,
the conservation of momentum equation is:
in the formula (11), rho is the density of the drilling fluid, A is the effective sectional area of the annulus, v is the flow velocity of the drilling fluid in the annulus, t is time,
the pressure wave velocity is calculated by equation (12),
in the formula (12), c is the pressure wave velocity;
step 3, calculating the water hammer pressure and flow rate by using multiphase flow parameters (including A, etc.), pressure wave velocity and a multiphase water hammer transient pressure model, wherein the multiphase water hammer transient pressure model comprises formulas (13) to (15), calculating the throttle opening by using a multiphase water hammer pressure inversion throttle opening model,
the two characteristic line equations are: dx/dt ═ v ± c (13)
The positive difference equation can be obtained along the positive direction of the characteristic line:
c+:Hi+1=Hi-B(Qi+1-Qi)-RQi|Qi| (14)
the negative difference equation can be obtained along the opposite direction of the characteristic line:
c-:Hi=Hi+1-B(Qi-Qi+1)+RQi+1|Qi+1| (15)
in the formulae (13) to (15), B is the transfer parameter value c/(g.A), and R is the transfer parameter value f.DELTA.x/(2. g.D.A)2),HiIs the water head pressure, D is the pipe diameter, f is the friction coefficient, c + is along the v + c direction, c-is along the v-c direction,
considering the flow coefficient and the opening coefficient, a multiphase water hammer pressure inversion throttle valve opening model is provided, wherein,
the model of the opening flow of the multi-phase water hammer pressure inversion throttle valve comprises the following steps:
the model of the opening of the multi-phase water hammer pressure inversion throttle valve is as follows:
in the formula (17), τ (j) is the throttle opening, Q is the throttle flow, and TmaxThe pressure time is limited by the throttle valve, delta t is the throttle valve adjusting interval, zeta is the throttle valve flow coefficient, and O is the opening coefficient;
because the throttle valve adjusting process is a continuous curve, the throttle valve opening calculated according to the multiphase water hammer pressure inversion throttle valve opening model is a scatter point, therefore, the throttle valve opening is fitted by adopting a cubic spline function interpolation method, and a three-turn square cubic spline fitting throttle valve opening model is constructed as follows:
in the formula (18), αj(x)、βj(x) For the interpolated void fraction and slip speed for each flow pattern,
between two nodes [ x ]j,xj+1]Above, the throttle opening (parameter curve) is expressed as:
in the formula (19), hjStep size, xjNode variable, mjObtained using boundary conditions.
After the control method disclosed by the invention is used for controlling the opening of the throttle valve, the effect of limiting the back pressure fluctuation can be achieved, the back pressure control of the pressure control drilling wellhead is stable, the problems of overflow and well leakage of a narrow density window possibly caused by the overshoot of the throttle valve can be avoided, the drilling complexity is reduced, and the pressure control of a shaft is more refined.
Drawings
FIG. 1 is a graph showing the change in back pressure when the back pressure is limited to 0.9 MPa.
FIG. 2 is a graph showing the change in back pressure when the back pressure is limited to 0.8 MPa.
FIG. 3 is a graph showing the change in back pressure when the back pressure is limited to 0.7 MPa.
FIG. 4 is a graph showing the change in back pressure when the back pressure is limited to 0.6 MPa.
FIG. 5 is a pressure wave velocity grid plot.
FIG. 6 is a schematic diagram of the technical idea of the control method of the pressure limiting and regulating valve for pressure controlled drilling based on cubic spline curve.
Detailed Description
The present invention is not limited by the following examples, and specific embodiments may be determined according to the technical solutions and practical situations of the present invention.
The invention is further described below with reference to the following examples:
example 1: as shown in fig. 6, the control method of the pressure-limiting and regulating valve for pressure-controlled drilling based on the cubic spline curve includes adjusting the opening of the throttle valve to control the wellhead back pressure when gas-liquid two-phase flow flows through the pressure-controlled drilling wellhead throttle valve, calculating the opening value of the throttle valve by using the limited wellhead back pressure to combine a wellbore multiphase flow model, a wellbore multiphase water hammer pressure model, a multiphase water hammer transient pressure model and a multiphase water hammer pressure inversion throttle opening model before adjusting the opening of the throttle valve, fitting the opening value of the throttle valve through the cubic spline fitting throttle valve opening model to obtain a throttle valve action curve, and adjusting the opening of the throttle valve according to the throttle valve action curve;
the throttle opening value and the throttle action curve are obtained according to the following method:
the oil-gas-drilling fluid three-phase fluid continuous equation is as follows:
in the formula (1), A is the annular cross-sectional area, rhokIs the density of the oil phase, the gas phase and the drilling liquid phase, phikVolume fractions of oil phase, gas phase and drilling liquid phase, vkIs the oil/gas/drilling fluid phase velocity, k is the oil phase gas phase and the drilling fluid phase, t is the time, s is the annulus length,
the oil-gas-drilling fluid three-phase fluid momentum conservation is as follows:
in the formula (2), g is gravity acceleration; p is a radical offGradient of friction resistance,
Dispersing the annulus into N grids, and solving the grids one by one along the well bottom to the well head, wherein the continuous equation differential format of the drilling fluid is as follows:
the spillover oil continuity equation difference format is as follows:
considering gas phase solubility, the overflow gas phase continuous equation difference format is as follows:
the difference format of the conservation of momentum equation is as follows:
in the formula (6), the first and second groups,
in the formula (9), vsm、vso、vsgSlip velocity, rho, of drilling fluid, formation oil and formation gas, respectivelym、ρo、ρgDensity of drilling fluid, formation oil and formation gas respectively;
taking an annular infinitesimal section as a control body, wherein the motion equation is as follows:
in the formula (10), p is pressure (back pressure), g is gravity acceleration, s is well length along the annulus, theta is the included angle between the annulus and the horizontal plane, and tauoIs the friction stress of the drilling fluid to the annular hollow wall, X is the control body wet circumference,
the conservation of momentum equation is:
in the formula (11), rho is the density of the drilling fluid, A is the effective sectional area of the annulus, v is the flow velocity of the drilling fluid in the annulus, t is time,
the pressure wave velocity is calculated by equation (12),
in the formula (12), c is the pressure wave velocity, and the pressure wave velocity meshing diagram is shown in FIG. 5;
step 3, calculating the water hammer pressure and flow rate by using multiphase flow parameters (including A, etc.), pressure wave velocity and a multiphase water hammer transient pressure model, wherein the multiphase water hammer transient pressure model comprises formulas (13) to (15), calculating the throttle opening by using a multiphase water hammer pressure inversion throttle opening model,
the two characteristic line equations are: dx/dt ═ v ± c (13)
The positive difference equation can be obtained along the positive direction of the characteristic line:
c+:Hi+1=Hi-B(Qi+1-Qi)-RQi|Qi| (14)
the negative difference equation can be obtained along the opposite direction of the characteristic line:
c-:Hi=Hi+1-B(Qi-Qi+1)+RQi+1|Qi+1| (15)
in the formulae (13) to (15), B is the transfer parameter value c/(g.A), and R is the transfer parameter value f.DELTA.x/(2. g.D.A)2),HiIs the water head pressure, D is the pipe diameter, f is the friction coefficient, c + is along the v + c direction, c-is along the v-c direction,
considering the flow coefficient and the opening coefficient, a multiphase water hammer pressure inversion throttle valve opening model is provided, wherein,
the model of the opening flow of the multi-phase water hammer pressure inversion throttle valve comprises the following steps:
the model of the opening of the multi-phase water hammer pressure inversion throttle valve is as follows:
in the formula (17), τ (j) is the throttle opening, Q is the throttle flow, and TmaxThe pressure time is limited by the throttle valve, delta t is the throttle valve adjusting interval, zeta is the throttle valve flow coefficient, and O is the opening coefficient;
because the throttle valve adjusting process is a continuous curve, the throttle valve opening calculated according to the multiphase water hammer pressure inversion throttle valve opening model is a scatter point, therefore, the throttle valve opening is fitted by adopting a cubic spline function interpolation method, and a three-turn square cubic spline fitting throttle valve opening model is constructed as follows:
in the formula (18), αj(x)、βj(x) For interpolation, the void ratio and slip speed (instantaneous speed) under each flow pattern are within two node intervals [ x ]j,xj+1]Above, the throttle opening (parameter curve) is expressed as:
in the formula (19), hjStep size, xjNode variable, mjObtained using boundary conditions.
mjThe method is obtained by combining boundary conditions with a multiphase water hammer transient pressure model, a multiphase water hammer pressure inversion throttle opening flow model, a multiphase water hammer pressure inversion throttle opening model and a cubic spline fitting throttle opening model.
Wellbore multiphase flow modeling is well known in the art.
Example 2: when the limited back pressure is 0.9MPa, the back pressure changes as shown in fig. 1 after throttle opening control is performed according to the control method described in embodiment 1.
Example 3: when the limited back pressure is 0.8MPa, the back pressure changes as shown in fig. 2 after the throttle opening degree control is performed according to the control method described in embodiment 1.
Example 4: when the limited back pressure is 0.7MPa, the back pressure changes as shown in fig. 3 after the throttle opening degree control is performed according to the control method described in embodiment 1.
Example 5: when the limited back pressure is 0.6MPa, the back pressure changes as shown in fig. 4 after the throttle opening degree control is performed according to the control method described in embodiment 1.
As can be seen from fig. 1 to 4, after the control method of the present invention is used to control the opening of the throttle valve, the effect of limiting the back pressure fluctuation can be achieved.
The invention provides a multiphase water hammer pressure inversion throttle valve opening model, a flow coefficient and an opening coefficient for the first time.
After the control method disclosed by the invention is used for controlling the opening of the throttle valve, the effect of limiting the back pressure fluctuation can be achieved, the back pressure control of the pressure control drilling wellhead is stable, the problems of overflow and well leakage of a narrow density window possibly caused by the overshoot of the throttle valve can be avoided, the drilling complexity is reduced, and the pressure control of a shaft is more refined.
The technical characteristics form an embodiment of the invention, which has strong adaptability and implementation effect, and unnecessary technical characteristics can be increased or decreased according to actual needs to meet the requirements of different situations.
Claims (2)
1. A control method of pressure-control drilling pressure-limiting regulation valve based on cubic spline curve is characterized by comprising the steps of adjusting the opening degree of a throttle valve to control the back pressure of a well mouth when gas-liquid two-phase flow flows through a pressure-control drilling well mouth throttle valve, calculating the opening degree of the throttle valve by utilizing the limited well mouth back pressure in combination with a well bore multiphase flow model, a well bore multiphase water attack pressure model, a multiphase water attack transient pressure model and a multiphase water attack pressure inversion throttle opening degree model before or during the adjustment of the opening degree of the throttle valve, fitting the opening degree of the throttle valve through cubic spline fitting to obtain a throttle valve action curve, and adjusting the opening degree of the throttle valve according to the throttle valve action curve.
2. The control method of the cubic spline-based pressure-controlled drilling pressure-limiting and regulating valve according to claim 1, wherein the throttle opening value and the throttle action curve are obtained by the following method:
step 1, inputting pressure-controlled drilling wellhead related original data into a wellbore multiphase flow model, wherein the original data comprises wellhead annulus sectional area, densities of an oil phase, a gas phase and a drilling liquid phase, volume fractions of the oil phase, the gas phase and the drilling liquid phase, speeds of the oil phase, the gas phase and the drilling liquid phase and annulus length, the wellbore multiphase flow model comprises formulas (1) to (6), and multiphase flow parameters are calculated through the wellbore multiphase flow model,
the oil-gas-drilling fluid three-phase fluid continuous equation is as follows:
in the formula (1), A is the annular cross-sectional area, rhokIs the density of the oil phase, the gas phase and the drilling liquid phase, phikVolume fractions of oil phase, gas phase and drilling liquid phase, vkIs the oil/gas/drilling fluid phase velocity, k is the oil phase gas phase and the drilling fluid phase, t is the time, s is the annulus length,
the oil-gas-drilling fluid three-phase fluid momentum conservation is as follows:
in the formula (2), g is gravity acceleration; p is a radical offIn order to obtain the friction gradient, the friction gradient is adopted,
dispersing the annulus into N grids, and solving the grids one by one along the well bottom to the well head, wherein the continuous equation differential format of the drilling fluid is as follows:
the spillover oil continuity equation difference format is as follows:
the overflow gas phase continuous equation difference format is as follows:
the difference format of the conservation of momentum equation is as follows:
in the formula (6), the first and second groups,
in the formula (9), vsm、vso、vsgSlip velocity, rho, of drilling fluid, formation oil and formation gas, respectivelym、ρo、ρgDensity of drilling fluid, formation oil and formation gas respectively;
step 2, calculating the multiphase pressure wave velocity by using a shaft multiphase water hammer pressure model, wherein the shaft multiphase water hammer pressure model is as follows:
taking an annular infinitesimal section as a control body, wherein the motion equation is as follows:
in the formula (10), p is pressure, g is gravity acceleration, s is well length along the annulus, theta is the included angle between the annulus and the horizontal plane, and tauoIs the friction stress of the drilling fluid to the annular hollow wall, X is the control body wet circumference,
the conservation of momentum equation is:
in the formula (11), rho is the density of the drilling fluid, A is the effective sectional area of the annulus, v is the flow velocity of the drilling fluid in the annulus, t is time,
the pressure wave velocity is calculated by equation (12),
in the formula (12), c is the pressure wave velocity;
step 3, calculating the water hammer pressure and flow rate by using the multiphase flow parameters, the pressure wave velocity and the multiphase water hammer transient pressure model, wherein the multiphase water hammer transient pressure model comprises formulas (13) to (15), calculating the throttle opening by using the multiphase water hammer pressure inversion throttle opening model,
the two characteristic line equations are: dx/dt ═ v ± c (13)
The positive difference equation can be obtained along the positive direction of the characteristic line:
c+:Hi+1=Hi-B(Qi+1-Qi)-RQi|Qi| (14)
the negative difference equation can be obtained along the opposite direction of the characteristic line:
c-:Hi=Hi+1-B(Qi-Qi+1)+RQi+1|Qi+1| (15)
in the formulae (13) to (15), B is the transfer parameter value c/(g.A), and R is the transfer parameter value f.DELTA.x/(2. g.D.A)2),HiIs the water head pressure, D is the pipe diameter, f is the friction coefficient, c + is along the v + c direction, c-is along the v-c direction,
the model of the opening flow of the multi-phase water hammer pressure inversion throttle valve comprises the following steps:
the model of the opening of the multi-phase water hammer pressure inversion throttle valve is as follows:
in the formula (17), τ (j) is the throttle opening, Q is the throttle flow, and TmaxFor throttle valve limiting pressure time, Δ t is throttle valve adjustment interval, ζ is throttle valve flow coefficient, and O is opening systemCounting;
step 4, fitting the throttle opening degree value by utilizing a cubic spline fitting throttle opening degree model to obtain a throttle opening degree action curve,
the cubic spline fitting throttle opening model is as follows:
in the formula (18), αj(x)、βj(x) For the interpolated void fraction and slip speed for each flow pattern,
between two nodes [ x ]j,xj+1]Above, the throttle opening is expressed as:
in the formula (19), hjStep size, xjNode variable, mjObtained using boundary conditions.
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Cited By (2)
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CN112901144A (en) * | 2021-03-11 | 2021-06-04 | 西南石油大学 | Special structure well shaft overflow dynamic characteristic analysis method |
CN114963014A (en) * | 2022-06-10 | 2022-08-30 | 国家石油天然气管网集团有限公司 | Natural gas conveying consumption reduction method for optimizing valve opening degree and reducing fluctuation pressure |
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