CN114818535A - Horizontal gas well liquid holdup calculation method based on flow pattern conversion boundary - Google Patents

Horizontal gas well liquid holdup calculation method based on flow pattern conversion boundary Download PDF

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CN114818535A
CN114818535A CN202210440415.5A CN202210440415A CN114818535A CN 114818535 A CN114818535 A CN 114818535A CN 202210440415 A CN202210440415 A CN 202210440415A CN 114818535 A CN114818535 A CN 114818535A
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罗程程
高丽蓉
刘永辉
杨建英
王强
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Abstract

The invention provides a horizontal gas well liquid holdup calculation method based on a flow pattern conversion boundary, which comprises the following steps: the method comprises the steps of constructing a three-parameter equation according to the trend that the liquid holdup rate changes along with the airflow rate, substituting the calculated liquid holdup rates of an annular flow-stirring flow conversion point, a stirring flow-slug flow conversion point, a slug flow-bubble flow conversion point and a corresponding airflow rate into the equation under the normal pressure/normal temperature condition at a certain wellbore liquid flow rate, iteratively solving the coefficients of the three-parameter equation, correcting the liquid holdup rate of a vertical section by using an angle correction term to obtain a new model of the liquid holdup rate at a certain inclination angle under normal temperature and normal pressure, converting the gas flow rate under high pressure into the corresponding airflow rate under normal pressure by using a dimensionless criterion based on a flow similarity criterion, and substituting the converted corresponding airflow rate under normal pressure into the new model to obtain the liquid holdup rate of the horizontal gas well under a certain pressure condition. The method does not need a large number of model comparison optimization and flow pattern judgment calculation, can directly calculate the liquid holdup of the whole well casing of the horizontal gas well according to the gas phase apparent flow rate, and is simple, convenient and accurate.

Description

Horizontal gas well liquid holdup calculation method based on flow pattern conversion boundary
Technical Field
The invention belongs to the technical field of gas well drainage and gas production, and particularly relates to a horizontal gas well liquid holdup calculation method based on a flow pattern conversion boundary.
Background
The water production obviously rises from the development of the gas reservoir to the middle and later stages, and the timely carrying of the liquid out of the shaft is an important measure for maintaining the normal production of the gas well and prolonging the life cycle. The gravity drop dominated by the liquid holdup is an important component of the wellbore pressure gradient and is also a key parameter in the continuous liquid carrying design of the gas well. Therefore, accurate prediction of the liquid holdup is the key for determining the pressure drop of the wellbore of the gas well and realizing continuous liquid carrying of the gas well.
At present, there are many methods for calculating the liquid holdup, including physical model methods, empirical formula methods, experimental test methods, and the like. The empirical or semi-empirical model is usually based on experimental tests and is only suitable for the conditions within the range of experimental parameters, and model evaluation is preferably performed in the calculation process. The mechanism model selects a corresponding calculation method after flow pattern recognition, however, flow pattern discrimination standards established by different scholars are different, so that the calculation result has large precision difference and poor engineering applicability.
In addition, the calculation method is mainly established on a vertical well, a horizontal well is divided into a vertical section, an inclined section and a horizontal section, a well inclination angle is continuously changed from 90 degrees to 0 degrees, flow pattern distribution is complex and changeable, and the influence of factors such as the change of the well inclination angle and the pipe diameter is more obvious. Therefore, a simple, convenient and practical unified liquid holdup calculation model aiming at the whole shaft of the horizontal well is lacked at present.
The invention provides a three-parameter model for calculating the liquid holdup of a horizontal well according to the gas phase apparent flow rate, which does not need a large amount of model comparison optimization and flow pattern judgment calculation, is suitable for engineering calculation, and provides an idea for simply, conveniently and accurately predicting the liquid holdup of the whole shaft of the horizontal well and the shaft pressure drop.
Disclosure of Invention
Aiming at the defects of the existing calculation method, the invention provides a calculation method for the liquid holdup of a horizontal gas well by constructing a three-parameter equation of which the liquid holdup changes along with the gas flow rate based on a flow pattern conversion limit.
In order to achieve the purpose, the invention provides the following technical scheme:
the method comprises the following steps: acquiring parameters such as pressure, temperature, inclination angle, air flow rate, liquid flow rate, pipe diameter, gas relative density and the like of a certain position of a gas well shaft;
step two: constructing a three-parameter equation of which the liquid holding rate changes along with the airflow rate;
H L ＝Av SG B +C (1)
in the formula, H L The liquid holdup of the vertical section is dimensionless; v. of SG Is the superficial gas flow rate, m/s; A. b, C are all model coefficients and are dimensionless.
Step three: calculating the liquid holding rate and the corresponding gas flow rate value of a ring flow-churning flow transition point, a churning flow-slug flow transition point, a slug flow-bubble flow transition point in a vertical pipe under the normal pressure/normal temperature condition (0.1MPa, 20 ℃) when the gas well shaft liquid flow rate is constant;
(1) the annular flow-agitated flow transition point corresponds to the air flow rate:
Figure BDA0003613762670000021
in the formula, v A-C The annular flow-churning flow transition point corresponds to the air flow rate, m/s; f. of i -internal friction factor, dimensionless; rho G, standard condition 、ρ L, standard condition of -gas and liquid density under standard conditions (0.1MPa, 20 ℃), kg/m 3 (ii) a g-acceleration of gravity, 9.8; r is 0 -tubing radius, m; delta-liquid film thickness, m.
Calculating an internal friction factor by adopting a Fore model:
Figure BDA0003613762670000022
in the formula, Re G Gas Reynolds number, dimensionless.
The liquid film thickness calculation formula is as follows:
Figure BDA0003613762670000023
in the formula Q L Flow rate of liquid, m 3 /s；μ L Liquid viscosity, mPas.
The annular flow-agitated flow transition point corresponds to the liquid holdup:
Figure BDA0003613762670000024
in the formula, H A-C The annular flow-stirring flow transition point corresponds to the liquid holdup and is dimensionless; d is the diameter of the oil pipe, m.
Then the relationship between the liquid holdup at the transition point of the annular flow and the turbulent flow and the gas flow rate can be obtained:
H A-C ＝Av A-C B +C (6)
(2) the liquid holdup corresponding to the churn flow-slug flow transition point and the slug flow-bubble flow transition point is respectively
H C-S ＝0.22 (7)
H S-B ＝0.75 (8)
In the formula, H C-S 、H S-B The stirring flow-slug flow transition point and the slug flow-bubble flow transition point correspond to liquid holdup and are dimensionless.
Calculating the airflow speed at the churn-slug flow transition point by using a Hasan-Kabir model:
v C-S ＝[0.0051(ρ l, standard condition v SL 2 ) 1.7 /ρ G, standard condition ] 0.5 (when ρ) L, standard condition of v SL 2 < 74.4 hours) (9)
Or
v C-S ＝[(25.41gρ L, standard condition v SL 2 -38.9)/ρ G, standard condition ] 0.5 (when ρ) L, standard condition v SL 2 > 74.4) (10)
In the formula, v C-S -the churn-slug transition point corresponds to the airflow rate, m/s; v. of SL -superficial liquid flow velocity, m/s; sigma-gas-water interfacial tension, N/m;
calculating the airflow speed of a slug flow-bubble flow transition point by adopting a drift model:
Figure BDA0003613762670000031
in the formula, v S-B -the slug flow-bubble flow transition point corresponds to the air flow rate, m/s; v. of SL -superficial liquid flow velocity, m/s; sigma-gas-water interfacial tension, N/m;
then the churn-slug flow transition point and slug-bubbly flow transition point liquid holdup rate versus gas flow rate can be obtained:
H C-S ＝Av C-S B +C (12)
H S-B ＝Av S-B B +C (13)
step four: calculating coefficients of the three parameter equation A, B, C;
the coefficients a and C are eliminated by combining equations (6), (12), and (13):
Figure BDA0003613762670000032
the equation (14) is modified and a function f (B) is introduced with respect to the coefficient B, as follows:
Figure BDA0003613762670000033
the function f (B) in the formula (15) is a nonlinear equation about B, and an iterative method is adopted to solve the following problems:
(1) judging the B value range according to the monotonous characteristic of a three-parameter equation of which the liquid holding rate changes along with the airflow speed: calculating f (0.001) × f (2), if f (0.001) × f (2) > 0, the initial value B is in the interval [ -1, -0.001], and let a be-1; b is-0.001; otherwise, in the interval [0.001,1], let a equal to 0.001; b is 1;
(2) let c ═ a + b)2, and calculate f (c);
(3) if f (c) is less than 0.0001 (precision requirement), if B ═ c, the iterative computation is ended, otherwise, the next computation is continued;
(4) if f (c) x f (b) is greater than 0, let a ═ c; if f (c) x f (b) < 0, repeat steps (2) to (3) with b ═ c;
then solving the model coefficients A and C:
Figure BDA0003613762670000041
C＝H S-B -Av S-B B (17)
step five: and carrying out angle correction on the calculation result of the liquid holdup of the vertical section by adopting an angle correction relational expression to obtain the liquid holdup value of the inclination angle, wherein the angle correction relational expression is a new model proposed according to an experimental test result:
H θ ＝H L sin 0.252 (1.364θ+0.262)/0.91 (18)
in the formula, H θ The liquid holdup at an inclination angle theta is dimensionless; theta-Angle of inclination, rad.
Step six: the gas flow rate at high pressure is converted to a corresponding gas flow rate at normal pressure using a dimensionless criterion based on a flow similarity criterion.
Calculating the gas density under pressure and temperature conditions at a given gas well wellbore location:
Figure BDA0003613762670000042
where rho-gas density under a given temperature and pressure, kg/m 3 ；γ g -gas relative density, dimensionless; z is gas compression factor, dimensionless; p-pressure, MPa; t-temperature, K;
Figure BDA0003613762670000043
after transformation there is the relation:
Figure BDA0003613762670000044
in the formula, Fr G Froude dimensionless norm, dimensionless; rho G, high pressure 、ρ L, high pressure Gas, liquid density under high pressure, kg/m 3 ；v SG, high pressure -the superficial gas flow rate at high pressure, m/s; v. of SG, standard conditions -apparent gas flow rate under standard conditions (0.1MPa, 20 ℃), m/s.
Step seven: the converted gas flow velocity v at normal pressure is corresponding to the gas flow velocity v SG, standard conditions And substituting the obtained gas flow into the new model obtained in the step five to obtain the liquid holdup of the horizontal gas well under a certain pressure condition.
Drawings
FIG. 1 is a schematic diagram showing the trend of liquid holding rate with airflow rate.
FIG. 2 is a flow chart of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further fully and fully described below.
Firstly, acquiring parameters such as pressure, temperature, inclination angle, airflow speed, liquid flow speed, pipe diameter, gas relative density and the like of a certain position of a gas well shaft;
step two: constructing a three-parameter equation according to the variation trend of the liquid holding rate along with the airflow speed:
H L ＝Av SG B +C (1)
in the formula, H L The liquid holdup of the vertical section is dimensionless; v. of SG Is the superficial gas flow rate, m/s; A. b, C are all model coefficients and are dimensionless.
Step three: calculating the liquid holding rate and the corresponding gas flow rate value of a ring flow-churning flow transition point, a churning flow-slug flow transition point, a slug flow-bubble flow transition point in a vertical pipe under the normal pressure/normal temperature condition (0.1MPa, 20 ℃) when the gas well shaft liquid flow rate is constant;
(1) the annular flow-churn flow transition point corresponds to the airflow rate:
Figure BDA0003613762670000051
in the formula, v A-C The annular flow-churning flow transition point corresponds to the air flow rate, m/s; f. of i -internal friction factor, dimensionless; rho G, standard condition 、ρ L, standard condition -gas and liquid density under standard conditions (0.1MPa, 20 ℃), kg/m 3 (ii) a g-acceleration of gravity, 9.8; r is 0 -tubing radius, m; delta-liquid film thickness, m.
Calculating an internal friction factor by adopting a Fore model:
Figure BDA0003613762670000052
in the formula, Re G Gas Reynolds number, dimensionless.
The liquid film thickness calculation formula is as follows:
Figure BDA0003613762670000053
in the formula, Q L Flow rate of liquid, m 3 /s；μ L Liquid viscosity, mPas.
The annular flow-churn flow transition point corresponds to the liquid holdup:
Figure BDA0003613762670000061
in the formula, H A-C The annular flow-stirring flow transition point corresponds to the liquid holdup and is dimensionless; d is the diameter of the oil pipe, m.
Then the relationship between the liquid holdup at the transition point of the annular flow and the turbulent flow and the gas flow rate can be obtained:
H A-C ＝Av A-C B +C (6)
(2) the liquid holdup corresponding to the churn flow-slug flow transition point and the slug flow-bubble flow transition point is respectively
H C-S ＝0.22 (7)
H S-B ＝0.75 (8)
In the formula, H C-S 、H S-B The stirring flow-slug flow transition point and the slug flow-bubble flow transition point correspond to liquid holdup and are dimensionless.
Calculating the gas flow rate at the churn-slug flow transition point by using a Hasan-Kabir model:
v C-S ＝[0.0051(ρ l, standard condition v SL 2 ) 1.7 /ρ G, standard condition ] 0.5 (when ρ) L, standard condition v SL 2 < 74.4 hours) (9)
Or
v C-S ＝[(25.41gρ L, standard condition v SL 2 -38.9)/ρ G, standard condition ] 0.5 (when ρ) L, standard condition v SL 2 > 74.4) (10)
In the formula, v C-S -the churn-slug transition point corresponds to the airflow rate, m/s; v. of SL -superficial liquid flow velocity, m/s; sigma-gas-water interfacial tension, N/m;
calculating the airflow speed of a slug flow-bubble flow transition point by adopting a drift model:
Figure BDA0003613762670000062
in the formula, v S-B -the slug flow-bubble flow transition point corresponds to the air flow rate, m/s; v. of SL -superficial liquid flow velocity, m/s; sigma-gas-water interfacial tension, N/m;
then the churn-slug flow transition point and slug-bubbly flow transition point liquid holdup rate versus gas flow rate can be obtained:
H C-S ＝Av C-S B +C (12)
H S-B ＝Av S-B B +C (13)
step four: calculating coefficients of the three parameter equation A, B, C;
combining the annular flow-churning flow transition point, churning flow-slug transition point, and slug-bubbly flow transition point liquid holdup versus gas flow rate eliminates coefficients a and C to give:
Figure BDA0003613762670000071
the expression (2) is modified and a function f (B) is introduced with respect to the coefficient B, as follows:
Figure BDA0003613762670000072
the function f (B) in the formula (15) is a nonlinear equation about B, and an iterative method is adopted to solve the following problems:
(1) judging the B value range according to the monotonous characteristic of a three-parameter equation of which the liquid holding rate changes along with the airflow speed: calculating f (0.001) × f (2), if f (0.001) × f (2) > 0, the initial value B is in the interval [ -1, -0.001], and let a be-1; b is-0.001; otherwise, if the position is in the interval [0.001,1], the value of a is made to be 0.001; b is 1;
(2) let c ═ a + b)2, and calculate f (c);
(3) if f (c) is less than 0.0001 (precision requirement), if B ═ c, the iterative computation is ended, otherwise, the next computation is continued;
(4) if f (c) x f (b) is greater than 0, let a be c; if f (c) x f (b) < 0, repeat steps (2) to (3) with b ═ c;
then solving the model coefficients A and C:
Figure BDA0003613762670000073
C＝H S-B -Av S-B B (17)
step five: and carrying out angle correction on the calculation result of the liquid holdup of the vertical section by adopting an angle correction relational expression to obtain the liquid holdup value of the inclination angle, wherein the angle correction relational expression is a new model proposed according to an experimental test result:
H θ ＝H L sin 0.252 (1.364θ+0.262)/0.91 (18)
in the formula, H θ The liquid holdup at an inclination angle theta is dimensionless; theta-Angle of inclination, rad.
Step six: converting the gas flow rate under high pressure into the corresponding gas flow rate under normal pressure by using a dimensionless criterion based on a flow similarity criterion;
(1) calculating the gas density under pressure and temperature conditions at the well bore location of a given gas well:
Figure BDA0003613762670000074
where rho-gas density under a given temperature and pressure, kg/m 3 ；γ g -gas relative density, dimensionless; z is gas compression factor, dimensionless; p-pressure, MPa; t-temperature, K;
(2) the dimensionless norm is used for converting the gas flow rate under high pressure:
Figure BDA0003613762670000081
after conversion, the air flow rate at normal pressure is:
Figure BDA0003613762670000082
in the formula, Fr G Froude dimensionless norm, dimensionless; rho G, high pressure 、ρ L, high pressure Gas, liquid density under high pressure, kg/m 3 ；v SG, high pressure -the superficial gas flow rate at high pressure, m/s; v. of SG, standard conditions -apparent gas flow rate under standard conditions (0.1MPa, 20 ℃), m/s.
Step seven: the converted gas flow velocity v at normal pressure is corresponding to the gas flow velocity v SG, standard conditions And substituting the obtained gas flow into the new model obtained in the step five to obtain the liquid holdup of the horizontal gas well under a certain pressure condition.
It should be understood that the above description is only exemplary of the invention in its specific application and is not intended to limit the invention to the particular forms disclosed, since any modification, equivalent replacement or improvement made within the spirit and scope of the invention should be considered in all respects.

Claims (4)

1. A horizontal gas well liquid holdup calculation method based on a flow pattern conversion limit is characterized by mainly comprising the following steps:
the method comprises the following steps: acquiring parameters such as pressure, temperature, inclination angle, air flow rate, liquid flow rate, pipe diameter, gas relative density and the like of a certain position of a gas well shaft;
step two: constructing a three-parameter equation of which the liquid holding rate changes along with the airflow rate;
step three: calculating the liquid holding rate and the corresponding gas flow rate value of a ring flow-churning flow transition point, a churning flow-slug flow transition point, a slug flow-bubble flow transition point in a vertical pipe under the normal pressure/normal temperature condition (0.1MPa, 20 ℃) when the gas well shaft liquid flow rate is constant;
step four: calculating coefficients of the three parameter equation A, B, C;
step five: carrying out angle correction on the calculation result of the liquid holdup of the vertical section by adopting an angle correction relational expression to obtain a new liquid holdup calculation model of the inclination angle;
step six: converting the gas flow rate under high pressure into the corresponding gas flow rate under normal pressure by using a dimensionless criterion based on a flow similarity criterion;
step seven: the converted gas flow velocity v at normal pressure is corresponding to the gas flow velocity v SG, standard conditions And substituting the new model obtained in the step five to obtain the liquid holdup of the horizontal gas well under a certain pressure condition.
2. The method for calculating the liquid holdup of the horizontal gas well based on the flow pattern conversion boundary as claimed in claim 1, wherein the method comprises the following steps: step two, constructing a three-parameter equation with the liquid holding rate changing along with the airflow rate, wherein the three-parameter equation comprises the following specific steps:
H L ＝Av SG B +C (1)
in the formula, H L The liquid holdup of the vertical section is dimensionless; v. of SG Is the superficial gas flow rate, m/s; A. b, C are all model coefficients and are dimensionless.
3. The method for calculating the liquid holdup of the horizontal gas well based on the flow pattern conversion boundary as claimed in claim 1, wherein the method comprises the following steps: in the fourth step, the model coefficient B is iteratively solved, specifically as follows: combining the annular flow-churning flow transition point, churning flow-slug transition point, and slug-bubbly flow transition point liquid holdup versus gas flow rate eliminates coefficients a and C to give:
Figure FDA0003613762660000011
the expression (2) is modified and a function f (B) is introduced with respect to the coefficient B, as follows:
Figure FDA0003613762660000012
the function f (B) in the formula (15) is a nonlinear equation about B, and an iterative method is adopted to solve the following problems:
(1) judging the B value range according to the monotonous characteristic of a three-parameter equation of which the liquid holding rate changes along with the airflow speed: calculating f (0.001) × f (2), if f (0.001) × f (2) > 0, the initial value B is in the interval [ -1, -0.001], and let a be-1; b is-0.001; otherwise, if the position is in the interval [0.001,1], the value of a is made to be 0.001; b is 1;
(2) let c ═ a + b)/2, and calculate f (c);
(3) if | f (c) | < 0.0001 (precision requirement), if B ═ c, the iterative computation is ended, otherwise, the next computation is continued;
(4) if f (c) x f (b) is greater than 0, let a be c; if f (c) x f (b) < 0, repeat steps (2) to (3) with b ═ c;
then solving the model coefficients A and C:
Figure FDA0003613762660000021
C＝H S-B -Av S-B B (5)
4. the method for calculating the liquid holdup of the horizontal gas well based on the flow pattern conversion boundary as claimed in claim 1, wherein the method comprises the following steps: and step five, carrying out angle correction on the calculation result of the liquid holdup of the vertical section by adopting an angle correction relational expression to obtain the liquid holdup value of the inclination angle, wherein the angle correction relational expression is a new model provided according to an experimental test result:
H θ ＝H L sin 0.252 (1.364θ+0.262)/0.91 (6)
in the formula, H θ The liquid holdup at an inclination angle theta is dimensionless; theta-Angle of inclination, rad.
CN202210440415.5A 2022-04-25 2022-04-25 Horizontal gas well liquid holdup calculation method based on flow pattern conversion boundary Pending CN114818535A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115012925A (en) * 2022-08-08 2022-09-06 西南石油大学 Experimental determination method for vertical gas well shaft flow pattern under high pressure condition
CN117454063A (en) * 2023-12-26 2024-01-26 西南石油大学 Wellbore oil-gas-water multiphase flow state discrimination and water holdup calculation method

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115012925A (en) * 2022-08-08 2022-09-06 西南石油大学 Experimental determination method for vertical gas well shaft flow pattern under high pressure condition
US11773714B1 (en) 2022-08-08 2023-10-03 Southwest Petroleum University Experimental method for determining flow patterns in vertical wellbore of gas wells at high-pressure conditions
CN117454063A (en) * 2023-12-26 2024-01-26 西南石油大学 Wellbore oil-gas-water multiphase flow state discrimination and water holdup calculation method
CN117454063B (en) * 2023-12-26 2024-03-12 西南石油大学 Wellbore oil-gas-water multiphase flow state discrimination and water holdup calculation method

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