CN112727438B - Annular pressure drop calculation method suitable for long open hole section of ultra-deep well - Google Patents

Annular pressure drop calculation method suitable for long open hole section of ultra-deep well Download PDF

Info

Publication number
CN112727438B
CN112727438B CN202110004857.0A CN202110004857A CN112727438B CN 112727438 B CN112727438 B CN 112727438B CN 202110004857 A CN202110004857 A CN 202110004857A CN 112727438 B CN112727438 B CN 112727438B
Authority
CN
China
Prior art keywords
fluid
formula
section
sampling point
avg
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202110004857.0A
Other languages
Chinese (zh)
Other versions
CN112727438A (en
Inventor
曾德智
罗江
汤明
石建刚
易浩
喻智明
李双贵
蒋振兴
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Southwest Petroleum University
Original Assignee
Southwest Petroleum University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Southwest Petroleum University filed Critical Southwest Petroleum University
Priority to CN202110004857.0A priority Critical patent/CN112727438B/en
Publication of CN112727438A publication Critical patent/CN112727438A/en
Application granted granted Critical
Publication of CN112727438B publication Critical patent/CN112727438B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
    • E21B—EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B21/00—Methods or apparatus for flushing boreholes, e.g. by use of exhaust air from motor
    • E21B21/08—Controlling or monitoring pressure or flow of drilling fluid, e.g. automatic filling of boreholes, automatic control of bottom pressure

Landscapes

  • Engineering & Computer Science (AREA)
  • Geology (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Mining & Mineral Resources (AREA)
  • Physics & Mathematics (AREA)
  • Environmental & Geological Engineering (AREA)
  • Fluid Mechanics (AREA)
  • General Life Sciences & Earth Sciences (AREA)
  • Geochemistry & Mineralogy (AREA)
  • Mechanical Engineering (AREA)
  • Geophysics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Earth Drilling (AREA)

Abstract

The invention discloses an annular pressure drop calculation method suitable for a long open hole section of an ultra-deep well, and belongs to the technical field of petroleum and natural gas drilling. The method is characterized in that: firstly, collecting ultra-deep well drill string data and logging curve data, enabling irregular open holes to be equivalent to elliptical well holes, and screening to obtain cross sections of various sample points, so as to determine the annular fluid overflowing area and wetted perimeter length of each cross section; further calculating the equivalent hydraulic diameter and the average axial flow velocity to obtain an average shear rate, thereby obtaining a corrected fluidity index; further calculating the effective consistency coefficient, the yield value and the shear rate to obtain the effective viscosity; and further calculating a Reynolds number value of the annular flow to obtain a Vanning friction parameter, and finally calculating the laminar annular flow pressure drop of the open hole section. The method has simple numerical calculation process, can quickly and accurately predict the annular pressure drop of irregular open holes, and is favorable for calculating the optimal and rapid drilling parameters of the ultra-deep well.

Description

Annular pressure drop calculation method suitable for long open hole section of ultra-deep well
Technical Field
The invention relates to the technical field of petroleum and natural gas drilling, in particular to an annulus pressure drop calculation method suitable for a long open hole section of an ultra-deep well.
Background
With the continuous increase of social energy demand, the development degree requirement of deep oil and gas resources with complex geological conditions and high exploitation difficulty is higher and higher, and the drilling technology of deep wells and ultra-deep wells still needs to be further perfected and developed. The calculation of the annulus pressure drop of the ultra-deep well is one of the core contents of drilling hydraulic parameter design, if the error between the calculation or prediction result and the actual annulus pressure drop is large, complex underground accidents such as well leakage, borehole wall instability, stuck drilling and the like are easily caused, and the drilling cost is increased, so that the method is necessary for meeting the practical application of engineering and quickly and accurately predicting the annulus pressure drop of the long open hole section of the ultra-deep well.
Currently, in the research of the method for calculating the annular pressure drop of the ultra-deep well, the 'method and system for predicting the bottom hole pressure' (application publication number: CN 109854237B) mainly consider the influence of the volume concentration of drill cuttings in the annular space and calculate the effective density of drilling fluid and the drilling fluid rheological parameters when the drill cuttings are contained, thereby determining the annular pressure drop and realizing the purpose of effectively predicting the bottom hole pressure; the method mainly considers the flow state of drilling fluid in the eccentric circular tube annulus power law fluid (application publication No. CN 101498214B), provides a method for calculating the Reynolds number of any gap of the cross section of the eccentric circular tube annulus, and calculates the regional angles of laminar flow and turbulent flow of the eccentric circular tube annulus. However, in the actual drilling process, the well hole is usually elliptical under the action of factors such as non-uniform ground stress, and except for elliptical well hole simulation which is difficult to apply on site, the conventional annular pressure drop calculation method usually considers a regular circular well hole, so that a certain error exists between the calculation result of the section and the underground actual annular pressure drop, and when the annular pressure drop of the elliptical well hole of the ultra-deep well is calculated, the accumulated error is larger, and the underground complex accident is more easily caused.
Disclosure of Invention
In view of the above problems, the present invention aims to provide an annulus pressure drop calculation method suitable for a long open hole section of an ultra-deep well, so as to solve the problem that the existing ultra-deep well has a large error in the calculation of the annulus pressure drop of the elliptical well under the action of factors such as non-uniform ground stress, etc., and the numerical calculation process is simple, so that the annulus pressure drop of the irregular open hole can be rapidly and accurately predicted, and the safety of drilling operation is improved.
The invention adopts the following technical scheme that the method for calculating the annular pressure drop of the long open hole section of the ultra-deep well is characterized by comprising the following steps of:
the method comprises the following steps: according to the collected ultra-deep well drill string data and the specific logging curve data, the irregular open hole is equivalent to an elliptical well hole, k sample point sections are analyzed and screened out, and the long axis length a of the open hole at the ith sample point section is determinediMinor axis length biDrill string radius ri(i ═ 1,2,3, …, k-1, k) and the annulus flow distance l between the ith and (i + 1) th sample cross-sectionsi(i＝1,2,3,…,k-1)；
Step two: the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting formula (1) to obtain the annular fluid flow area A at the section of the ith sampling pointi；
Ai＝πaibi-πri 2(i＝1,2,3,…,k-1,k) (1)
In the formula: a. theiIs the annular fluid flow area m at the section of the ith sampling point2；aiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiThe radius of a drill string at the section of the ith sampling point is m;
the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting the formula (2) to obtain the length L of the wetted perimeter at the section of the ith sampling pointi；
Li＝π(ai+bi)+2πri(i＝1,2,3,…,k-1,k) (2)
In the formula: l isiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiThe radius of a drill string at the section of the ith sampling point is m;
step three: the annular fluid flow area A at the section of the ith sampling point in the second stepiAnd wet circumference length LiSubstituting into formula (3) to calculate the equivalent hydraulic diameter D of the naked eyeavg；
Figure BDA0002882810670000021
In the formula: davgThe equivalent hydraulic diameter of the naked eye, m; a. theiIs the annular fluid flow area m at the section of the ith sampling point2；LiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown;
the annular fluid flow area A at the section of the ith sampling point in the second stepiSubstituting the formula (4) into the formula to calculate the average axial flow velocity v of the naked eyeavg；
Figure BDA0002882810670000022
In the formula: v. ofavgThe average axial flow velocity of the naked eye is m/s; a. theiIs the annular fluid flow area m at the section of the ith sampling point2(ii) a Q is the annular fluid flow, m3/s；
Step four: the equivalent hydraulic diameter D of the naked eye in the third stepavgAnd bore hole average axial flow velocity vavgSubstituting the obtained product into formula (5) to calculate the average shear rate gamma of the fluid in the open holeavg；
Figure BDA0002882810670000023
In the formula: gamma rayavgThe average shear rate of the fluid in the open hole is 1/s; davgThe equivalent hydraulic diameter of the naked eye, m; v. ofavgThe average axial flow velocity of the naked eye is m/s;
step five: averaging the shear rate gamma of the bare hole fluid in the fourth stepavgSubstituting the modified fluidity index m into a formula (6) to calculate a modified fluidity index m;
Figure BDA0002882810670000024
in the formula: m is a corrected fluidity index and is dimensionless; n is a fluidity index and is dimensionless; k is the fluid consistency coefficient, Pa · Sn；γavgThe average shear rate of the fluid in the open hole is 1/s; tau isyIs the fluid yield value, Pa;
step six: substituting the corrected fluidity index m in the step five into a formula (7) to calculate the effective fluid consistency coefficient Kef；
Figure BDA0002882810670000031
In the formula: kefIs a fluid effective consistency coefficient, Pa · Sn(ii) a K is the fluid consistency coefficient, Pa · Sn(ii) a m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (8) to calculate the effective yield value tau of the fluidef；
Figure BDA0002882810670000032
In the formula: tau isefIs the fluid effective yield value, Pa; tau isyIs the fluid yield value, Pa; m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (9) to calculate the effective shearing rate gamma of the fluidef；
Figure BDA0002882810670000033
In the formula: gamma rayef1/s, which is the effective shear rate of the fluid; gamma rayavgIs the average shear rate of the fluid, 1/s; m is a corrected fluidity index and is dimensionless;
step seven: the effective consistency coefficient K of the fluid in the step sixefEffective yield value of fluidefAnd effective shear rate gamma of the fluidefSubstituting into formula (10) to calculate the effective viscosity eta of the fluidef；
ηef＝τef·γef -1+Kef·γef n-1 (10)
In the formula: etaefPa/s for the effective viscosity of the fluid; kefIs a fluid effective consistency coefficient, Pa · Sn；τefIs the fluid effective yield value, Pa; gamma rayef1/s, which is the effective shear rate of the fluid; n is a fluidity index and is dimensionless;
step eight: the effective viscosity eta of the fluid in the step sevenefSubstituting the Reynolds number into the formula (11), and calculating the Reynolds number Re of the open hole annular flow;
Figure BDA0002882810670000034
in the formula: re is the Reynolds number of open hole annular flow, and is dimensionless; rho is the fluid density, kg/m3；vavgThe average axial flow velocity of the naked eye is m/s; davgThe equivalent hydraulic diameter of the naked eye, m; etaefPa/s for the effective viscosity of the fluid;
step nine: substituting the open hole annular flow Reynolds number Re in the step eight into a formula (12) to calculate a fanning friction parameter f;
Figure BDA0002882810670000035
in the formula: f is fanning friction parameter without dimension; re is the Reynolds number of annular flow, and is dimensionless;
step ten: the annular flow distance l between the section of the ith sampling point in the step one and the section of the (i + 1) th sampling pointi(i is 1,2,3, …, k-2, k-1) is substituted into the formula (14) to calculate the annular flow distance delta L, and the fanning friction parameter f in the step nine is substituted into the formula (13) to calculate the open hole laminar flow annular spaceA flow pressure drop Δ P;
Figure BDA0002882810670000041
wherein:
Figure BDA0002882810670000042
in the formula: delta P is the pressure drop of the open-hole laminar flow annulus flow, Pa; f is fanning friction parameter without dimension; v. ofavgThe average axial flow velocity of the naked eye is m/s; Δ L is the annulus flow distance, m; davgThe equivalent hydraulic diameter of the naked eye, m; liThe annulus flow distance, m, between the ith sample point cross section and the (i + 1) th sample point cross section.
Further, the value range of the annular flow distance delta L is 1-9 m.
Furthermore, the value range of the number k of the cross sections of the sampling points is 5-100.
Due to the adoption of the technical scheme, the invention has the following advantages:
(1) according to the method, the annular fluid overflowing area when the elliptical borehole changes is calculated in a segmented mode according to the ultra-deep well drill column data and the logging curve data, and the accuracy of calculation of the annular pressure drop of the ultra-deep well is improved.
(2) The method simplifies the calculation process of the annular pressure drop of the ultra-deep well by introducing a mode of correcting the fluidity index and the effective viscosity of the annular fluid.
Drawings
FIG. 1 is a flow chart of an annulus pressure drop calculation method suitable for a long open hole section of an ultra-deep well.
Detailed Description
The invention is described in detail below with reference to the drawings and the detailed description.
As shown in FIG. 1, the method for calculating the annular pressure drop suitable for the long open hole section of the ultra-deep well provided by the invention comprises the following steps:
the method comprises the following steps: according to the collected ultra-deep well drill string data and well loggingThe specific data of the curve is obtained by equating irregular open hole to elliptical borehole, analyzing and screening k sample point sections, and determining the major axis length a of the open hole at the ith sample point sectioniMinor axis length biDrill string radius ri(i ═ 1,2,3, …, k-1, k) and the annulus flow distance l between the ith and (i + 1) th sample cross-sectionsi(i＝1,2,3,…,k-1)；
Step two: the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting formula (1) to obtain the annular fluid flow area A at the section of the ith sampling pointi；
Ai＝πaibi-πri 2(i＝1,2,3,…,k-1,k) (1)
In the formula: a. theiIs the annular fluid flow area m at the section of the ith sampling point2；aiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiThe radius of a drill string at the section of the ith sampling point is m;
the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting the formula (2) to obtain the length L of the wetted perimeter at the section of the ith sampling pointi；
Li＝π(ai+bi)+2πri(i＝1,2,3,…,k-1,k) (2)
In the formula: l isiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiThe radius of a drill string at the section of the ith sampling point is m;
step three: the annular fluid flow area A at the section of the ith sampling point in the second stepiAnd wet circumference length LiSubstituting into formula (3) to calculate the equivalent hydraulic diameter D of the naked eyeavg；
Figure BDA0002882810670000051
In the formula: davgThe equivalent hydraulic diameter of the naked eye, m; a. theiIs the annular fluid flow area m at the section of the ith sampling point2；LiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown;
the annular fluid flow area A at the section of the ith sampling point in the second stepiSubstituting the formula (4) into the formula to calculate the average axial flow velocity v of the naked eyeavg；
Figure BDA0002882810670000052
In the formula: v. ofavgThe average axial flow velocity of the naked eye is m/s; a. theiIs the annular fluid flow area m at the section of the ith sampling point2(ii) a Q is the annular fluid flow, m3/s；
Step four: the equivalent hydraulic diameter D of the naked eye in the third stepavgAnd bore hole average axial flow velocity vavgSubstituting the obtained product into formula (5) to calculate the average shear rate gamma of the fluid in the open holeavg；
Figure BDA0002882810670000053
In the formula: gamma rayavgThe average shear rate of the fluid in the open hole is 1/s; davgThe equivalent hydraulic diameter of the naked eye, m; v. ofavgThe average axial flow velocity of the naked eye is m/s;
step five: averaging the shear rate gamma of the bare hole fluid in the fourth stepavgSubstituting the modified fluidity index m into a formula (6) to calculate a modified fluidity index m;
Figure BDA0002882810670000054
in the formula: m is a corrected fluidity index and is dimensionless; n is a fluidity index and is dimensionless; k is the fluid consistency coefficient, Pa · Sn；γavgThe average shear rate of the fluid in the open hole is 1/s; tau isyIs the fluid yield value, Pa;
step six: substituting the corrected fluidity index m in the step five into a formula (7) to calculate the effective fluid consistency coefficient Kef；
Figure BDA0002882810670000055
In the formula: kefIs a fluid effective consistency coefficient, Pa · Sn(ii) a K is the fluid consistency coefficient, Pa · Sn(ii) a m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (8) to calculate the effective yield value tau of the fluidef；
Figure BDA0002882810670000061
In the formula: tau isefIs the fluid effective yield value, Pa; tau isyIs the fluid yield value, Pa; m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (9) to calculate the effective shearing rate gamma of the fluidef；
Figure BDA0002882810670000062
In the formula: gamma rayef1/s, which is the effective shear rate of the fluid; gamma rayavgIs the average shear rate of the fluid, 1/s; m is a corrected fluidity index and is dimensionless;
step seven: the effective consistency coefficient K of the fluid in the step sixefEffective yield value of fluidefAnd effective shear rate gamma of the fluidefSubstituting into formula (10) to calculate the effective viscosity eta of the fluidef；
ηef＝τef·γef -1+Kef·γef n-1 (10)
In the formula: etaefPa/s for the effective viscosity of the fluid; kefIs a fluid effective consistency coefficient, Pa · Sn；τefIs the fluid effective yield value, Pa; gamma rayef1/s, which is the effective shear rate of the fluid; n is a fluidity index and is dimensionless;
step eight: the effective viscosity eta of the fluid in the step sevenefSubstituting the Reynolds number into the formula (11), and calculating the Reynolds number Re of the open hole annular flow;
Figure BDA0002882810670000063
in the formula: re is the Reynolds number of open hole annular flow, and is dimensionless; rho is the fluid density, kg/m3；vavgThe average axial flow velocity of the naked eye is m/s; davgThe equivalent hydraulic diameter of the naked eye, m; etaefPa/s for the effective viscosity of the fluid;
step nine: substituting the open hole annular flow Reynolds number Re in the step eight into a formula (12) to calculate a fanning friction parameter f;
Figure BDA0002882810670000064
in the formula: f is fanning friction parameter without dimension; re is the Reynolds number of annular flow, and is dimensionless;
step ten: the annular flow distance l between the section of the ith sampling point in the step one and the section of the (i + 1) th sampling pointi(i is 1,2,3, …, k-2, k-1) is substituted into the formula (14) to calculate the annular flow distance delta L, and the fanning friction parameter f in the step nine is substituted into the formula (13) to calculate the open hole laminar flow annular flow pressure drop delta P;
Figure BDA0002882810670000065
wherein:
Figure BDA0002882810670000071
in the formula: delta P is the pressure drop of the open-hole laminar flow annulus flow, Pa; f is fanning friction parameter without dimension; v. ofavgThe average axial flow velocity of the naked eye is m/s; Δ L is the annulus flow distance, m; davgThe equivalent hydraulic diameter of the naked eye, m; liThe annulus flow distance, m, between the ith sample point cross section and the (i + 1) th sample point cross section.
Further, the value range of the annular flow distance delta L is 1-9 m.
Furthermore, the value range of the number k of the cross sections of the sampling points is 5-100.
The following examples are provided to further illustrate the embodiments of the present invention and are not intended to limit the scope of the present invention.
Example (b):
an annulus pressure drop calculation method suitable for a long open hole section of an ultra-deep well comprises the following steps:
the method comprises the following steps: according to the collected ultra-deep well drill string data and the specific logging curve data, the irregular open hole is equivalent to an elliptical well hole, 5 sample point sections are analyzed and screened out, and the long axis length a of the open hole at each sample point section is determinediMinor axis length biDrill string radius ri(i ═ 1,2,3,4,5) and the annular flow distance l between the ith and the (i + 1) th spot cross-sectionsi(i ═ 1,2,3,4) in m, and the data are as follows:
(a1,b1,r1,)＝(0.112,0.093,0.070)，(a2,b2,r2)＝(0.135,0.121,0.070)，
(a3,b3,r3)＝(0.115,0.098,0.070)，(a4,b4,r4)＝(0.108,0.108,0.070)，
(a1,b1,r1)＝(0.141,0.126,0.070)，(l1,l2,l3,l4)＝(0.11,0.26,0.35,0.58)；
step two: the length a of the long axis of the naked eye at the cross section of the 5 sampling points in the step oneiMinor axis length biAnd drill string radius ri(i is 1,2,3,4,5) and substituting the formula (1) to respectively obtain the annular fluid flow area A at the section of each point1＝0.017m2，A2＝0.036m2，A3＝0.020m2，A4＝0.021m2，A5＝0.040m2，；
The length a of the long axis of the naked eye at the cross section of the 5 sampling points in the step oneiMinor axis length biAnd drill string radius ri(i is 1,2,3,4,5) and substituting the formula (2) to obtain wet circumference length L at each point section1＝1.084m，L2＝1.244m，L3＝1.109m，L4＝1.118m，L5＝1.279m；
Step three: the annular fluid flow area A at the cross section of the 5 sampling points in the step twoiAnd wet circumference length LiSubstituting (i-1, 2,3,4,5) into formula (3) to calculate the open hole equivalent hydraulic diameter Davg＝0.095m；
The annular fluid flow area A at the cross section of the 5 sampling points in the step twoi(i-1, 2,3,4,5) and a known parameter annulus fluid flow Q-0.02 m3Substituting the/s into the formula (4) to calculate the average axial flow velocity v of the naked eyeavg＝0.741m/s；
Step four: the equivalent hydraulic diameter D of the naked eye in the third stepavgAnd bore hole average axial flow velocity vavgSubstituting the obtained product into formula (5) to calculate the average shear rate gamma of the fluid in the open holeavg＝62.400 1/s；
Step five: averaging the shear rate gamma of the bare hole fluid in the fourth stepavgAnd the known parameters of fluidity index n being 0.58, fluid consistency coefficient K being 1.04 and fluid yield value tauySubstituting 10.42Pa into equation (6), and calculating the modified fluidity index m to be 0.303;
step six: substituting the corrected fluidity index m in the step five into a formula (7) to calculate the effective fluid consistency coefficient Kef＝2.756；
Substituting the corrected fluidity index m in the step five into a formula (8) to calculate the effective yield value tau of the fluidef＝27.615Pa；
Substituting the corrected fluidity index m in the step five into a formula (9) to calculate the effective shearing rate gamma of the fluidef＝165.370 1/s；
Step seven: the effective consistency coefficient K of the fluid in the step sixefEffective yield value of fluidefAnd effective shear rate gamma of the fluidefSubstituting into formula (10) to calculate the effective viscosity eta of the fluidef＝0.489Pa/s；
Step eight: the effective viscosity eta of the fluid in the step sevenefAnd the known parameter fluid density p is 1280kg/m3Substituting the equation (11) into the equation (11), and calculating an open hole annulus flow Reynolds number Re as 184.265;
step nine: substituting the open hole annular flow Reynolds number Re in the step eight into the formula (12), and calculating a fanning friction parameter f to be 0.087;
step ten: the annular flow distance l between the section of the ith sampling point in the step one and the section of the (i + 1) th sampling pointi(i is 1,2,3, …, k-2, k-1) and substituting equation (14) to calculate the annulus flow distance Δ L is 1.30m, and substituting fanning friction parameter f in the step nine into equation (13) to calculate the open hole laminar annulus flow pressure drop Δ P is 1673.460 Pa.
From the above calculations, the annulus pressure drop for an open hole annulus flow distance Δ L of 1.30m in the example was 1673.460 Pa.
The method considers the condition that the well hole is generally elliptical under the action of factors such as non-uniform ground stress and the like in the actual drilling process, adopts a method for calculating the annular fluid overflow area when the elliptical well hole is changed in a segmented mode and correcting the equivalent hydraulic diameter of the open hole, and introduces the corrected fluidity index and the effective viscosity of the annular fluid, so that the annular pressure drop calculation method suitable for the long open hole well section of the ultra-deep well is provided. The method can be used for quickly and accurately predicting the annular pressure drop of the long open hole section of the ultra-deep well based on the drill column data of the ultra-deep well, the logging curve data and the known engineering parameters, provides data support for the design of drilling hydraulic parameters, is beneficial to realizing the optimal and rapid drilling of the ultra-deep well and reduces the drilling cost.

Claims (3)

1. An annulus pressure drop calculation method suitable for a long open hole section of an ultra-deep well is characterized by comprising the following steps:
the method comprises the following steps: according to the collected ultra-deep well drill string data and the specific logging curve data, the irregular open hole is equivalent to an elliptical well hole, k sample point sections are analyzed and screened out, and the long axis length a of the open hole at the ith sample point section is determinediMinor axis length biDrill string radius ri(i ═ 1,2,3, …, k-1, k) and the annulus flow distance l between the ith and (i + 1) th sample cross-sectionsi(i＝1,2,3,…,k-1)；
Step two: the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting formula (1) to obtain the annular fluid flow area A at the section of the ith sampling pointi；
Ai＝πaibi-πri 2(i＝1,2,3,…,k-1,k) (1)
In the formula: a. theiIs the annular fluid flow area m at the section of the ith sampling point2；aiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiThe radius of a drill string at the section of the ith sampling point is m;
the length a of the long axis of the naked eye at the section of the ith sampling point in the first stepiMinor axis length biAnd drill string radius riSubstituting the formula (2) to obtain the length L of the wetted perimeter at the section of the ith sampling pointi；
Li＝π(ai+bi)+2πri(i＝1,2,3,…,k-1,k) (2)
In the formula: l isiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown; r isiIs the ith sampleRadius of drill string at point cross section, m;
step three: the annular fluid flow area A at the section of the ith sampling point in the second stepiAnd wet circumference length LiSubstituting into formula (3) to calculate the equivalent hydraulic diameter D of the naked eyeavg；
Figure FDA0002882810660000011
In the formula: davgThe equivalent hydraulic diameter of the naked eye, m; a. theiIs the annular fluid flow area m at the section of the ith sampling point2；LiThe length m of the wetted perimeter at the section of the ith sampling point; a isiThe length of a long axis m of a naked eye at the section of the ith sampling point; biThe minor axis length m of the naked eye at the section of the ith sampling point is shown;
the annular fluid flow area A at the section of the ith sampling point in the second stepiSubstituting the formula (4) into the formula to calculate the average axial flow velocity v of the naked eyeavg；
Figure FDA0002882810660000012
In the formula: v. ofavgThe average axial flow velocity of the naked eye is m/s; a. theiIs the annular fluid flow area m at the section of the ith sampling point2(ii) a Q is the annular fluid flow, m3/s；
Step four: the equivalent hydraulic diameter D of the naked eye in the third stepavgAnd bore hole average axial flow velocity vavgSubstituting the obtained product into formula (5) to calculate the average shear rate gamma of the fluid in the open holeavg；
Figure FDA0002882810660000021
In the formula: gamma rayavgThe average shear rate of the fluid in the open hole is 1/s; davgThe equivalent hydraulic diameter of the naked eye, m; v. ofavgMean axial direction for bare holeFlow velocity, m/s;
step five: averaging the shear rate gamma of the bare hole fluid in the fourth stepavgSubstituting the modified fluidity index m into a formula (6) to calculate a modified fluidity index m;
Figure FDA0002882810660000022
in the formula: m is a corrected fluidity index and is dimensionless; n is a fluidity index and is dimensionless; k is the fluid consistency coefficient, Pa · Sn；γavgThe average shear rate of the fluid in the open hole is 1/s; tau isyIs the fluid yield value, Pa;
step six: substituting the corrected fluidity index m in the step five into a formula (7) to calculate the effective fluid consistency coefficient Kef；
Figure FDA0002882810660000023
In the formula: kefIs a fluid effective consistency coefficient, Pa · Sn(ii) a K is the fluid consistency coefficient, Pa · Sn(ii) a m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (8) to calculate the effective yield value tau of the fluidef；
Figure FDA0002882810660000024
In the formula: tau isefIs the fluid effective yield value, Pa; tau isyIs the fluid yield value, Pa; m is a corrected fluidity index and is dimensionless;
substituting the corrected fluidity index m in the step five into a formula (9) to calculate the effective shearing rate gamma of the fluidef；
Figure FDA0002882810660000025
In the formula: gamma rayef1/s, which is the effective shear rate of the fluid; gamma rayavgIs the average shear rate of the fluid, 1/s; m is a corrected fluidity index and is dimensionless;
step seven: the effective consistency coefficient K of the fluid in the step sixefEffective yield value of fluidefAnd effective shear rate gamma of the fluidefSubstituting into formula (10) to calculate the effective viscosity eta of the fluidef；
ηef＝τef·γef -1+Kef·γef n-1 (10)
In the formula: etaefPa/s for the effective viscosity of the fluid; kefIs a fluid effective consistency coefficient, Pa · Sn；τefIs the fluid effective yield value, Pa; gamma rayef1/s, which is the effective shear rate of the fluid; n is a fluidity index and is dimensionless;
step eight: the effective viscosity eta of the fluid in the step sevenefSubstituting the Reynolds number into the formula (11), and calculating the Reynolds number Re of the open hole annular flow;
Figure FDA0002882810660000026
in the formula: re is the Reynolds number of open hole annular flow, and is dimensionless; rho is the fluid density, kg/m3；vavgThe average axial flow velocity of the naked eye is m/s; davgThe equivalent hydraulic diameter of the naked eye, m; etaefPa/s for the effective viscosity of the fluid;
step nine: substituting the open hole annular flow Reynolds number Re in the step eight into a formula (12) to calculate a fanning friction parameter f;
Figure FDA0002882810660000031
in the formula: f is fanning friction parameter without dimension; re is the Reynolds number of annular flow, and is dimensionless;
step ten: the annular flow distance l between the section of the ith sampling point in the step one and the section of the (i + 1) th sampling pointi(i is 1,2,3, …, k-2, k-1) is substituted into the formula (14) to calculate the annular flow distance delta L, and the fanning friction parameter f in the step nine is substituted into the formula (13) to calculate the open hole laminar flow annular flow pressure drop delta P;
Figure FDA0002882810660000032
wherein:
Figure FDA0002882810660000033
in the formula: delta P is the pressure drop of the open-hole laminar flow annulus flow, Pa; f is fanning friction parameter without dimension; v. ofavgThe average axial flow velocity of the naked eye is m/s; Δ L is the annulus flow distance, m; davgThe equivalent hydraulic diameter of the naked eye, m; liThe annulus flow distance, m, between the ith sample point cross section and the (i + 1) th sample point cross section.
2. The annular pressure drop calculation method suitable for the long open hole section of the ultra-deep well according to claim 1, is characterized in that: the value range of the annular flow distance delta L is 1-9 m.
3. The annular pressure drop calculation method suitable for the long open hole section of the ultra-deep well according to claim 1, is characterized in that: the value range of the number k of the cross sections of the sampling points is 5-100.
CN202110004857.0A 2021-01-04 2021-01-04 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well Active CN112727438B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110004857.0A CN112727438B (en) 2021-01-04 2021-01-04 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110004857.0A CN112727438B (en) 2021-01-04 2021-01-04 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well

Publications (2)

Publication Number Publication Date
CN112727438A CN112727438A (en) 2021-04-30
CN112727438B true CN112727438B (en) 2022-02-18

Family

ID=75589654

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110004857.0A Active CN112727438B (en) 2021-01-04 2021-01-04 Annular pressure drop calculation method suitable for long open hole section of ultra-deep well

Country Status (1)

Country Link
CN (1) CN112727438B (en)

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2001002832A1 (en) * 1999-07-06 2001-01-11 Sofitech N.V. Modelling the rheological behaviour of drilling fluids as a function of pressure and temperature
CN110929458A (en) * 2019-11-15 2020-03-27 长江大学 Method for calculating annulus comprehensive hydraulic equivalent diameter of irregular borehole section
CN111173489A (en) * 2020-01-06 2020-05-19 西南石油大学 Method for calculating free settling velocity of fiber-containing proppant clusters in fracture
EP3730926A1 (en) * 2019-04-26 2020-10-28 Helmholtz-Zentrum Potsdam - Deutsches GeoForschungsZentrum GFZ Stiftung des Öffentlichen Rechts des Lands Brandenburg Method and system for measuring or monitoring the viscosity of flowing materials

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2007145734A2 (en) * 2006-06-07 2007-12-21 Exxonmobil Upstream Research Company Compressible objects having partial foam interiors combined with a drilling fluid to form a variable density drilling mud
WO2008127237A1 (en) * 2007-04-12 2008-10-23 Halliburton Energy Services, Inc. Borehole characterization
US9394783B2 (en) * 2011-08-26 2016-07-19 Schlumberger Technology Corporation Methods for evaluating inflow and outflow in a subterranean wellbore
US9909413B2 (en) * 2014-05-14 2018-03-06 Board Of Regents, The University Of Texas System Systems and methods for determining a rheological parameter

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2001002832A1 (en) * 1999-07-06 2001-01-11 Sofitech N.V. Modelling the rheological behaviour of drilling fluids as a function of pressure and temperature
EP3730926A1 (en) * 2019-04-26 2020-10-28 Helmholtz-Zentrum Potsdam - Deutsches GeoForschungsZentrum GFZ Stiftung des Öffentlichen Rechts des Lands Brandenburg Method and system for measuring or monitoring the viscosity of flowing materials
CN110929458A (en) * 2019-11-15 2020-03-27 长江大学 Method for calculating annulus comprehensive hydraulic equivalent diameter of irregular borehole section
CN111173489A (en) * 2020-01-06 2020-05-19 西南石油大学 Method for calculating free settling velocity of fiber-containing proppant clusters in fracture

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Simplified modeling of YPL fluid flow through a concentric elliptical;Tang Ming等;《Journal of Petroleum Science and Engineering》;20171215;第225-232页 *
幂律流体螺旋层流流动压降简化模型;翟科军等;《石油机械》;20201031;第48卷(第10期);第22-26页 *
赫巴流体在圆管内层流流动理论及混凝土泵送应用实例;王衍伟等;《混凝土与水泥制品》;20180131;第10-15页 *

Also Published As

Publication number Publication date
CN112727438A (en) 2021-04-30

Similar Documents

Publication Publication Date Title
Jin et al. Characterization of oil/water two-phase flow patterns based on nonlinear time series analysis
CN112627733B (en) Method and equipment for optimizing hydraulic parameters of deepwater pressure-controlled drilling in real time
Delwiche et al. Slimhole drilling hydraulics
CN102787817A (en) Comprehensive simulation experimental device of drilling circulation system
CN105089639A (en) Dynamic prediction method for wellbore flow in coal-bed gas well
CN109598024A (en) The drilling well waterpower optimization method and equipment coupled based on wellbore cleaning with annular pressure
CN108829902A (en) A kind of appraisal procedure for tubing string hydraulic fracturing erosion damage
CN112727438B (en) Annular pressure drop calculation method suitable for long open hole section of ultra-deep well
Zhao et al. Combined control mechanism of weight on bit and rate of penetration with a downhole robot in the coiled-tubing drilling process
Igwilo et al. A Review on Gas Well Optimization Using Production Performance Models—A Case Study of Horizontal Well
Feng et al. Research on Water-conducting Fractured Zone height under the condition of large mining height in Yushen mining area, China
CN110929447A (en) Shaft temperature field numerical calculation method in thickening acid acidification process
Chowdhury et al. Analysis of cuttings concentration experimental data using exploratory data analysis
Yang et al. Estimating and optimizing wellbore pressure during primary cementing in low pressure and leakage formations
CN109812237B (en) Drilling fluid discharge capacity determination method meeting requirements for cleaning of special-shaped well hole
CN112651113A (en) Safe mud density window judgment method suitable for east China sea pressure failure stratum
CN109296358B (en) Well bore quality evaluation method for well cementation
Liu et al. Modeling fluctuating pressure in the eccentric annulus with a four-parameter rheological method
Zulqarnain et al. The effect of constant and variable eccentricity on the spacer performance during primary well cementing
Guo et al. Mechanical characteristics of cluster perforation string under running process in horizontal wells with unconventional oil/gas reservoirs
Xie et al. Improving Drilling Efficiency Using Intelligent Decision System for Drilling in Bohai Oilfield Based on Big Data
Silva et al. Application of conformal mapping in the calculation of geological pressures
Bakyani et al. Gas Condensate Wells Simulation to Optimize Well Flow Performance Using Tubing Equations Coupled with Inflow-Performance-Relation (IPR) Curve
Wang et al. Reservoir Development Principle
Salem et al. Drillpipe eccentricity prediction during drilling directional wells

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant