CN113323658B - Method for calculating leakage pressure of shaft - Google Patents

Method for calculating leakage pressure of shaft Download PDF

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CN113323658B
CN113323658B CN202110753840.5A CN202110753840A CN113323658B CN 113323658 B CN113323658 B CN 113323658B CN 202110753840 A CN202110753840 A CN 202110753840A CN 113323658 B CN113323658 B CN 113323658B
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superposition
formula
pressure
crack
density
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CN113323658A (en
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曾德智
罗江
汤明
张新
张思松
李双贵
易浩
于洋
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Southwest Petroleum University
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
    • E—FIXED CONSTRUCTIONS
    • E21—EARTH DRILLING; MINING
    • E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B47/00—Survey of boreholes or wells

Abstract

The invention discloses a method for calculating leakage pressure of a shaft, and belongs to the technical field of petroleum and natural gas drilling. The method is characterized in that: firstly, collecting relevant well logging and well drilling data, and determining a crack parameter to be drilled, a calculated point position parameter and an engineering allowable loss rate; then calculating the initial density of the drilling fluid, thereby obtaining the bottom hole pressure after the density of the drilling fluid is overlapped and updated; further establishing a drilling fluid flowing plane coordinate system in the fracture, thereby obtaining the single fracture leakage rate; and further calculating the total leakage rate of the horizontal section cracks, so as to judge whether the allowable leakage rate of the project is reached or not, and finally determining the leakage pressure of the calculated point of the shaft. The method can quickly and accurately predict the leakage pressure of the shaft, provide technical support for the drilling of the fractured formation and improve the safety of the underground operation.

Description

Method for calculating leakage pressure of shaft
Technical Field
The invention relates to the technical field of petroleum and natural gas drilling, in particular to a method for calculating leakage pressure of a shaft.
Background
Along with the continuous increase of the exploration and development strength of oil and gas resources, the damage caused by the well leakage in the well drilling process is increasingly prominent, particularly for fractured strata, the safety density window is narrow, the pressure bearing capacity is low, and the well leakage condition is serious when the well drilling is carried out in an overbalance mode. The lost circulation refers to the phenomenon that when the pressure of a liquid column in a shaft is higher than the pressure of formation fluid, drilling fluid leaks into formation pores or cracks. In order to avoid the occurrence of the lost circulation accident, the key point is whether the calculated lost circulation pressure is accurate, if the error between the prediction result and the actual formation lost circulation pressure is large, a large amount of drilling fluid is leaked into the formation, so that the complex accidents under the well, such as well collapse, blowout, stuck drill and the like, are caused, and therefore, the method which is convenient for the practical application of engineering and can quickly and accurately predict the lost circulation pressure of the shaft is necessary.
At present, in the research aiming at a shaft leakage pressure calculation method, a leakage pressure determination device and a storage medium (application publication number: CN 113027426A) mainly perform a stratum pressure bearing test on a plurality of shaft drilling well sections to obtain the safe annular pressure of the drilling well sections without leakage, determine the fracture pressure and annular pressure loss of each sampling point, and combine the leakage state of drilling fluid in the drilling well sections to determine the leakage pressure of a shaft to be drilled. A novel method for measuring stratum leakage pressure with a narrow safety density window (application publication No. CN 109458171A) is mainly characterized in that a method for increasing a casing pressure value to a designed casing pressure value by stopping a pump and closing a throttle valve is adopted, casing pressure change conditions are observed, a stable casing pressure value is obtained, and finally the stratum leakage pressure is calculated to be the sum of liquid column pressure and the stable casing pressure value.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a method for calculating wellbore leakage pressure, so as to solve the problem that it is difficult to accurately predict leakage pressure in the drilling process of fractured formations of the existing horizontal well, and the numerical calculation process is simple and convenient, and can effectively reduce the occurrence of downhole complex accidents.
The invention adopts the following technical scheme that a method for calculating the leakage pressure of a shaft is characterized by comprising the following steps of:
the method comprises the following steps: determining fracture parameters of a horizontal section to be drilled according to the collected adjacent well core and imaging logging information, wherein the fracture parameters comprise fracture width aeHeight of crack beDensity k of the crack lineeAnd crack length le(ii) a Selecting a leakage pressure calculation point and determining position parameters according to the drilling engineering design data, wherein the leakage pressure calculation point comprises a calculation point well depth L, a calculation point vertical depth H and a horizontal section length delta L; determining the allowable leakage rate of the project [ q ] according to the leakage condition of the adjacent well horizontal segment during the leakage stopping operationt]；
Step two: corresponding the calculated point in the step one to a pore pressure equivalent density rhopAnd a given pumping pressure equivalent density S1Safe added value S2Substituting the superposed value delta rho of the drilling fluid density into a formula (1) to obtain the initial density rho of the drilling fluid0；
ρ0＝ρp+S1+S2-Δρ (1)
In the formula: rho0Is the initial density of the drilling fluid in g/cm3；ρpIs pore pressure equivalent density, g/cm3；S1Is a pumping pressure equivalent density, g/cm3；S2G/cm for safe added value3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step three: the initial density rho of the drilling fluid in the step two0Substituting the drilling fluid density superposition value delta rho into a formula (2) to obtain the drilling fluid density rho after the ith superpositioni(i＝1,2,3,…，k)；
ρi＝ρ0+Δρ(i＝1,2,3,…,k) (2)
In the formula: rhoiThe density of the drilling fluid after the ith superposition is g/cm3；ρ0Is the initial density of the drilling fluid in g/cm3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step four: the density rho of the drilling fluid after the ith superposition in the third stepi(i is 1,2,3, …, k) and substituting into equation (3) to obtain annulus cyclic pressure drop Pc；
Figure BDA0003146753820000021
In the formula: pcAnnular circulation pressure drop, MPa; f is the friction coefficient of the annular fluid and is dimensionless; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a L is the calculated point well depth, m; q is the displacement, L/s; d is the borehole diameter, cm; d is the outer diameter of the pipe column, cm;
the density rho of the drilling fluid after the ith superposition in the third stepi(i ═ 1,2,3, …, k) and said annulus cyclic pressure drop PcSubstituting the obtained pressure into a formula (4) to obtain the bottom hole pressure P after the ith superpositionLi(i＝1,2,3,…,k)；
PLi＝0.0098ρiH+Pc(i＝1,2，3，…,k) (4)
In the formula: pLiThe bottom hole pressure after the ith superposition is MPa; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a H is the vertical depth of the calculation point m; pcAnnular circulation pressure drop, MPa;
step five: establishing a plane rectangular coordinate system by taking the starting point on one side of the crack as a coordinate origin O, the flowing direction of the drilling fluid as an x axis and the width direction of the crack as a y axis, dividing the drilling fluid in the crack into a region I, a region II and a region III along the y axis direction, and corresponding the calculated point to the pore pressure PpAnd in step four, the bottom hole pressure P after the i-th superpositionLi(i is 1,2,3, …, k) is substituted into the formula (5) to obtain the width t corresponding to the region IIp；
Figure BDA0003146753820000022
In the formula: t is tpArea II corresponds to width, mm; tau is0Is the fluid yield value, Pa; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m;
step six: the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and step (ii)Fifthly, the area II corresponds to the width tpSubstituting into formula (6) to obtain velocity profile v in y direction of fluid in region I1(y)；
Figure BDA0003146753820000023
In the formula: v. of1(y) is the velocity profile in the y direction of the fluid in zone I, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (7) to obtain velocity profile v in y direction of fluid in region II2(y)；
Figure BDA0003146753820000031
In the formula: v. of2(y) is the velocity profile in the y direction of the fluid in zone II, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (8) to obtain velocity profile v in y direction of fluid in region III3(y)；
Figure BDA0003146753820000032
In the formula: v. of3(y) is the velocity profile in the y direction of the fluid in zone III, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step seven: the velocity profile v in the y direction of the fluid in the area I in the sixth step1(y) is substituted into the formula (9) to carry out integration to obtain the flow q corresponding to the area I1；
Figure BDA0003146753820000033
In the formula: q. q.s1For zone I corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area II in the sixth step2(y) is substituted into the formula (10) to carry out integration to obtain the corresponding flow q of the area II2；
Figure BDA0003146753820000034
In the formula: q. q.s2For zone II corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area III in the sixth step3(y) is substituted into the formula (11) to carry out integration to obtain the flow q corresponding to the area III3；
Figure BDA0003146753820000041
In the formula: q. q.s3For zone III corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step eight: corresponding the area I in the step seven to the flow q1Flow rate q corresponding to region II2Flow rate q corresponding to region III3Substituting into formula (12) to obtain single crack loss rate qa；
qa＝q1+q2+q3 (12)
In the formula: q. q.saIs the single crack loss rate, m3/h；q1For zone I corresponding to flow, m3/h；q2For zone II corresponding to flow, m3/h；q3Corresponding flow q for zone III3，m3/h；
Step nine: subjecting the density k of the crack lines in the step oneeSubstituting the length delta L of the horizontal segment into a formula (13) to obtain the total leakage rate q of the horizontal segment after the ith superpositionti(i＝1,2,3,…,k)；
qti＝qakeΔL (13)
In the formula: q. q.stiIs the total leakage rate of the horizontal segment after the ith superposition, m3/h；qaIs the single crack loss rate, m3/h；keSplit line density, bars/m; Δ L is the horizontal segment length, m;
step ten: judging the total leakage rate q of the horizontal segment after the ith superpositionti(i-1, 2,3, …, k) is equal to the engineering allowed loss rate qt]If q isti≠[qt]Returning to the third step to calculate the drilling fluid density rho after the i +1 th superpositioni+1Repeating the fourth step to the tenth step; if q isti＝[qt]Determining the bottom hole pressure P after the ith superposition at the momentLiCorresponding leakage pressure P for the calculated pointfAnd ending the calculation.
Further, in the second step to the tenth step, the drilling fluid in the annulus and the fracture belongs to yield power law fluid.
Further, the value range of the density superposition value delta rho of the drilling fluid is 0.01-0.05 g/cm3。
Due to the adoption of the technical scheme, the invention has the following advantages:
(1) the method comprehensively considers the influence of factors such as stratum fracture parameters and drilling fluid performance, and the like, and determines the velocity profile and flow distribution condition of the drilling fluid in the fracture in the y direction in different areas, so that the accuracy of calculating the total leakage rate of the horizontal section is ensured.
(2) According to the method, the condition that the fractured stratum is allowed to have the well leakage is considered, the drilling fluid density is updated in a superposition mode, the total leakage rate of the horizontal section is equal to the engineering allowable leakage rate, the calculated point leakage pressure is determined, and the applicability of the method for calculating the fractured stratum leakage pressure is enhanced.
Drawings
FIG. 1 is a flow chart of a method of wellbore lost circulation pressure calculation;
FIG. 2 is a schematic diagram of a rectangular coordinate system of the drilling fluid flow plane within a fracture.
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 wellbore loss pressure provided by the invention comprises the following steps:
the method comprises the following steps: determining fracture parameters of a horizontal section to be drilled according to the collected adjacent well core and imaging logging information, wherein the fracture parameters comprise fracture width aeHeight of crack beDensity k of the crack lineeAnd crack length le(ii) a Selecting a leakage pressure calculation point and determining position parameters according to the drilling engineering design data, wherein the leakage pressure calculation point comprises a calculation point well depth L, a calculation point vertical depth H and a horizontal section length delta L; determining the allowable leakage rate of the project [ q ] according to the leakage condition of the adjacent well horizontal segment during the leakage stopping operationt]；
Step two: corresponding the calculated point in the step one to a pore pressure equivalent density rhopAnd a given pumping pressure equivalent density S1Safe added value S2Substituting the superposed value delta rho of the drilling fluid density into a formula (1) to obtain the initial density rho of the drilling fluid0；
ρ0＝ρp+S1+S2-Δρ (1)
In the formula: rho0Is the initial density of the drilling fluid in g/cm3；ρpIs pore pressure equivalent density, g/cm3；S1Is a pumping pressure equivalent density, g/cm3；S2G/cm for safe added value3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step three: the initial density rho of the drilling fluid in the step two0Substituting the drilling fluid density superposition value delta rho into a formula (2) to obtain the drilling fluid density rho after the ith superpositioni(i＝1,2，3,…,k)；
ρi＝ρ0+Δρ(i＝1,2,3,…,k) (2)
In the formula: rhoiThe density of the drilling fluid after the ith superposition is g/cm3；ρ0Is the initial density of the drilling fluid in g/cm3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step four: the density rho of the drilling fluid after the ith superposition in the third stepi(i is 1,2,3, …, k) and substituting into equation (3) to obtain annulus cyclic pressure drop Pc；
Figure BDA0003146753820000051
In the formula: pcAnnular circulation pressure drop, MPa; f is the friction coefficient of the annular fluid and is dimensionless; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a L is the calculated point well depth, m; q is the displacement, L/s; d is the borehole diameter, cm; d is the outer diameter of the pipe column, cm;
the density rho of the drilling fluid after the ith superposition in the third stepi(i ═ 1,2,3, …, k) and said annulus cyclic pressure drop PcSubstituting the obtained pressure into a formula (4) to obtain the bottom hole pressure P after the ith superpositionLi(i＝1,2，3，…，k)；
PLi＝0.0098ρiH+Pc(i＝1，2,3,…,k) (4)
In the formula: pLiThe bottom hole pressure after the ith superposition is MPa; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a H is the vertical depth of the calculation point m; pcAnnular circulation pressure drop, MPa;
step five: establishing a plane rectangular coordinate system by taking the starting point on one side of the crack as a coordinate origin O, the flowing direction of the drilling fluid as an x axis and the width direction of the crack as a y axis, dividing the drilling fluid in the crack into a region I, a region II and a region III along the y axis direction, and corresponding the calculated point to the pore pressure PpAnd in step four, the bottom hole pressure P after the i-th superpositionLi(i is 1,2,3, …, k) is substituted into the formula (5) to obtain the width t corresponding to the region IIp；
Figure BDA0003146753820000052
In the formula: t is tpArea II corresponds to width, mm; tau is0Is the fluid yield value, Pa; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m;
step six: the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (6) to obtain velocity profile v in y direction of fluid in region I1(y)；
Figure BDA0003146753820000061
In the formula: v. of1(y) is the velocity profile in the y direction of the fluid in zone I, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (7) to obtain velocity profile v in y direction of fluid in region II2(y)；
Figure BDA0003146753820000062
In the formula: v. of2(y) is the velocity profile in the y direction of the fluid in zone II, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (8) to obtain velocity profile v in y direction of fluid in region III3(y)；
Figure BDA0003146753820000063
In the formula: v. of3(y) is the velocity profile in the y direction of the fluid in zone III, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition，MPa；PpCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step seven: the velocity profile v in the y direction of the fluid in the area I in the sixth step1(y) is substituted into the formula (9) to carry out integration to obtain the flow q corresponding to the area I1；
Figure BDA0003146753820000064
In the formula: q. q.s1For zone I corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area II in the sixth step2(y) is substituted into the formula (10) to carry out integration to obtain the corresponding flow q of the area II2；
Figure BDA0003146753820000071
In the formula: q. q.s2For zone II corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area III in the sixth step3(y) is substituted into the formula (11) to carry out integration to obtain the flow q corresponding to the area III3；
Figure BDA0003146753820000072
In the formula: q. q.s3For zone III corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step eight: corresponding the area I in the step seven to the flow q1Flow rate q corresponding to region II2Flow rate q corresponding to region III3Substituting into formula (12) to obtain single crack loss rate qa；
qa＝q1+q2+q3 (12)
In the formula: q. q.saIs the single crack loss rate, m3/h；q1For zone I corresponding to flow, m3/h；q2For zone II corresponding to flow, m3/h；q3Corresponding flow q for zone III3，m3/h；
Step nine: subjecting the density k of the crack lines in the step oneeSubstituting the length delta L of the horizontal segment into a formula (13) to obtain the total leakage rate q of the horizontal segment after the ith superpositionti(i＝1,2,3,…,k)；
qti＝qakeΔL (13)
In the formula: q. q.stiIs the total leakage rate of the horizontal segment after the ith superposition, m3/h；qaIs the single crack loss rate, m3/h；keSplit line density, bars/m; Δ L is the horizontal segment length, m;
step ten: judging the total leakage rate q of the horizontal segment after the ith superpositionti(i-1, 2,3, …, k) is equal to the engineering allowed loss rate qt]If q isti≠[qt]Then returning to the third step to calculate the i +1 th superpositionDrilling fluid density of rhoi+1Repeating the fourth step to the tenth step; if q isti＝[qt]Determining the bottom hole pressure P after the ith superposition at the momentLiCorresponding leakage pressure P for the calculated pointfAnd ending the calculation.
Further, in the second step to the tenth step, the drilling fluid in the annulus and the fracture belongs to yield power law fluid.
Further, the value range of the density superposition value delta rho of the drilling fluid is 0.01-0.05 g/cm3。
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):
a wellbore lost circulation pressure calculation method comprising the steps of:
the method comprises the following steps: determining the width a of the crack to be drilled according to the collected adjacent well core and the imaging logging informatione0.2mm, crack height be0.5mm, density k of split linese0.25 pieces/m and crack length le2.5 m; selecting a calculation point well depth L of 4000m, a calculation point vertical depth H of 3800m and a horizontal section length Delta L of 54m according to the drilling engineering design data; the leakage rate of the adjacent well horizontal section reaches 5-7 m3The leakage stopping operation is needed, so that the allowable leakage rate q of the project is determinedt]＝6m3/h；
Step two: corresponding the calculated point in the step one to a pore pressure equivalent density rhop＝1.15g/cm3And a given pumping pressure equivalent density S1＝0.05g/cm3Safe added value S2＝0.04g/cm3And the superposition value delta rho of the drilling fluid density is 0.04g/cm3Substituting the initial density rho of the drilling fluid into the formula (1)0＝1.20g/cm3；
Step three: the initial density rho of the drilling fluid in the step two0Substituting the drilling fluid density superposition value delta rho into a formula (2) to obtain the drilling fluid density rho after the 1 st superposition1＝1.24g/cm3；
Step four: according to related drilling data, the friction coefficient f of the annular fluid is 0.03, the discharge capacity Q is 9L/s, the borehole diameter D is 15.4cm, and the outer diameter D of the tubular column is 8.89cm, and the drilling fluid density rho is calculated in combination with the point well depth L of 4000m in the first step and the drilling fluid density rho after the 1 st superposition in the third step1Substituting the annular pressure drop into formula (3) to obtain annular circulation pressure drop Pc＝2.62MPa；
The density rho of the drilling fluid after the 1 st superposition in the third step1And annular circulation pressure drop PcSubstituting into formula (4) to obtain bottom hole pressure P after 1 st superpositionL1＝48.80MPa；
Step five: establishing a plane rectangular coordinate system by taking the starting point of one side of the fracture as a coordinate origin O, the flow direction of the drilling fluid as an x axis and the width direction of the fracture as a y axis, and dividing the drilling fluid in the fracture into a region I, a region II and a region III along the y axis direction, wherein the yield value tau of the fluid is known0Calculating point corresponding to pore pressure P of 11MPap42.83MPa and the corresponding bottom hole pressure P in step fourLSubstituting the obtained value into formula (5) to obtain the corresponding width t of the region IIp＝0.09mm；
Step six: it is known that the fluidity index n is 0.5 and the fluid consistency factor K is 1Pa · SnCorresponding the calculated point in the fourth step to the bottom hole pressure PLAnd the width t corresponding to the area II in the step fivepRespectively substituting into formula (6), formula (7) and formula (8) to obtain velocity profile v in y direction of fluid in region I1(y) velocity profile v in region II in the y-direction of the fluid2(y) and the velocity profile v in the y-direction of the fluid in zone III3(y)；
Step seven: the velocity profile v in the y direction of the fluid in the area I in the sixth step1(y) is substituted into the formula (9) to carry out integration to obtain the flow q corresponding to the area I1＝0.022m3/h；
The velocity profile v in the y direction of the fluid in the area II in the sixth step2(y) is substituted into the formula (10) to carry out integration to obtain the flow q corresponding to the area II2＝0.049m3/h；
The velocity profile v in the y direction of the fluid in the area III in the sixth step3(y) is substituted into the formula (11) to be integratedObtaining the corresponding flow q of the region III3＝0.022m3/h；
Step eight: corresponding the area I in the step seven to the flow q1Flow rate q corresponding to region II2Flow rate q corresponding to region III3Substituting the obtained product into a formula (12) to obtain the single-crack leakage rate qa＝0.093m3/h；
Step nine: subjecting the density k of the crack lines in the step oneeSubstituting the length delta L of the horizontal segment into a formula (13) to obtain the total leakage rate q of the horizontal segment after the 1 st superpositionti＝1.256m3/h；
Step ten: according to the allowable loss rate [ q ] of the project in the step onet]＝6m3H, judging qt1≠[qt]Returning to the step three to calculate the drilling fluid density rho after the 2 nd superposition2＝1.28g/cm3Repeating the fourth to ninth steps to obtain the total leakage rate q of the 2 nd superposed horizontal segmentt2＝3.127m3H, judging qt2≠[qt](ii) a Returning to the step three to calculate the drilling fluid density rho after the 3 rd superposition3＝1.32g/cm3Repeating the fourth step to the tenth step to obtain the bottom hole pressure P after the 3 rd superpositionL351.95MPa, and total loss rate q of the horizontal segmentt3＝6.048m3H, approximate judgment is qt2＝[qt]Then determining the corresponding leakage pressure P of the calculated pointf＝PL3When the pressure is 51.95MPa, the calculation is finished.
Through the calculation, the leakage pressure P of the horizontal section at the well depth L of 4000m is obtained in the embodimentfIs 51.95 MPa.
The method considers the condition that certain well leakage is allowed in the actual drilling process of the fractured stratum, determines the velocity profile and the flow distribution condition of the drilling fluid in the fracture in regions, and updates the density of the drilling fluid in a circulating, overlapping and updating mode to enable the leakage rate of the horizontal section to be equal to the allowable leakage rate of engineering, so that the leakage pressure calculation method suitable for the horizontal section of the fractured stratum is provided. The method can quickly and accurately predict the leakage pressure of the horizontal section of the fractured stratum based on the adjacent well core, the imaging logging information and the known engineering parameters, provides technical support for safe drilling of the fractured stratum and avoids the occurrence of underground complex accidents.

Claims (3)

1. A method for calculating wellbore leak-off pressure, comprising the steps of:
the method comprises the following steps: determining fracture parameters of a horizontal section to be drilled according to the collected adjacent well core and imaging logging information, wherein the fracture parameters comprise fracture width aeHeight of crack beDensity k of the crack lineeAnd crack length le(ii) a Selecting a leakage pressure calculation point and determining position parameters according to the drilling engineering design data, wherein the leakage pressure calculation point comprises a calculation point well depth L, a calculation point vertical depth H and a horizontal section length delta L; determining the allowable leakage rate of the project [ q ] according to the leakage condition of the adjacent well horizontal segment during the leakage stopping operationt]；
Step two: corresponding the calculated point in the step one to a pore pressure equivalent density rhopAnd a given pumping pressure equivalent density S1Safe added value S2Substituting the superposed value delta rho of the drilling fluid density into a formula (1) to obtain the initial density rho of the drilling fluid0；
ρ0＝ρp+S1+S2-Δρ (1)
In the formula: rho0Is the initial density of the drilling fluid in g/cm3；ρpIs pore pressure equivalent density, g/cm3；S1Is a pumping pressure equivalent density, g/cm3；S2G/cm for safe added value3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step three: the initial density rho of the drilling fluid in the step two0Substituting the drilling fluid density superposition value delta rho into a formula (2) to obtain the drilling fluid density rho after the ith superpositioni(i＝1,2,3,…,k)；
ρi＝ρ0+Δρ(i＝1,2,3,…,k) (2)
In the formula: rhoiThe density of the drilling fluid after the ith superposition is g/cm3；ρ0Is the initial density of the drilling fluid in g/cm3(ii) a Delta rho is the density superposition value of the drilling fluid in g/cm3；
Step four: the density rho of the drilling fluid after the ith superposition in the third stepi(i is 1,2,3, …, k) and substituting into equation (3) to obtain annulus cyclic pressure drop Pc；
Figure FDA0003146753810000011
In the formula: pcAnnular circulation pressure drop, MPa; f is the friction coefficient of the annular fluid and is dimensionless; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a L is the calculated point well depth, m; q is the displacement, L/s; d is the borehole diameter, cm; d is the outer diameter of the pipe column, cm;
the density rho of the drilling fluid after the ith superposition in the third stepi(i ═ 1,2,3, …, k) and said annulus cyclic pressure drop PcSubstituting the obtained pressure into a formula (4) to obtain the bottom hole pressure P after the ith superpositionLi(i＝1,2,3,…,k)；
PLi＝0.0098ρiH+Pc(i＝1,2,3,…,k) (4)
In the formula: pLiThe bottom hole pressure after the ith superposition is MPa; rhoiThe density of the drilling fluid after the ith superposition is g/cm3(ii) a H is the vertical depth of the calculation point m; pcAnnular circulation pressure drop, MPa;
step five: establishing a plane rectangular coordinate system by taking the starting point on one side of the crack as a coordinate origin O, the flowing direction of the drilling fluid as an x axis and the width direction of the crack as a y axis, dividing the drilling fluid in the crack into a region I, a region II and a region III along the y axis direction, and corresponding the calculated point to the pore pressure PpAnd in step four, the bottom hole pressure P after the i-th superpositionLi(i is 1,2,3, …, k) is substituted into the formula (5) to obtain the width t corresponding to the region IIp；
Figure FDA0003146753810000021
In the formula: t is tpArea II corresponds to width, mm; tau is0Is a streamBulk yield value, Pa; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m;
step six: the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (6) to obtain velocity profile v in y direction of fluid in region I1(y)；
Figure FDA0003146753810000022
In the formula: v. of1(y) is the velocity profile in the y direction of the fluid in zone I, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and in step five said region II corresponds to width tpSubstituting into formula (7) to obtain velocity profile v in y direction of fluid in region II2(y)；
Figure FDA0003146753810000023
In the formula: v. of2(y) is the velocity profile in the y direction of the fluid in zone II, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the bottom hole pressure P after the i-th superposition in the step fourLi(i ═ 1,2,3, …, k) and said region II in step five correspond to each otherWidth tpSubstituting into formula (8) to obtain velocity profile v in y direction of fluid in region III3(y)；
Figure FDA0003146753810000024
In the formula: v. of3(y) is the velocity profile in the y direction of the fluid in zone III, m/s; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step seven: the velocity profile v in the y direction of the fluid in the area I in the sixth step1(y) is substituted into the formula (9) to carry out integration to obtain the flow q corresponding to the area I1；
Figure FDA0003146753810000025
In the formula: q. q.s1For zone I corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area II in the sixth step2(y) is substituted into the formula (10) to carry out integration to obtain the corresponding flow q of the area II2；
Figure FDA0003146753810000031
In the formula: q. q.s2For zone II corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
the velocity profile v in the y direction of the fluid in the area III in the sixth step3(y) is substituted into the formula (11) to carry out integration to obtain the flow q corresponding to the area III3；
Figure FDA0003146753810000032
In the formula: q. q.s3For zone III corresponding to flow, m3/h；beIs the crack height, m; n is a fluidity index and is dimensionless; pLiThe bottom hole pressure after the ith superposition is MPa; ppCalculating the corresponding pore pressure, MPa; leIs the crack length, m; k is the fluid consistency coefficient, Pa · Sn；aeIs the width of the crack, mm; t is tpArea II corresponds to width, mm;
step eight: corresponding the area I in the step seven to the flow q1Flow rate q corresponding to region II2Flow rate q corresponding to region III3Substituting into formula (12) to obtain single crack loss rate qa；
qa＝q1+q2+q3 (12)
In the formula: q. q.saIs the single crack loss rate, m3/h；q1For zone I corresponding to flow, m3/h；q2For zone II corresponding to flow, m3/h；q3Corresponding flow q for zone III3，m3/h；
Step nine: subjecting the density k of the crack lines in the step oneeSubstituting the length delta L of the horizontal segment into a formula (13) to obtain the total leakage rate q of the horizontal segment after the ith superpositionti(i＝1,2,3,…,k)；
qti＝qakeΔL (13)
In the formula: q. q.stiIs the total leakage rate of the horizontal segment after the ith superposition, m3/h；qaIs the single crack loss rate, m3/h；keSplit line density, bars/m; Δ L is the horizontal segment length, m;
step ten: judging the total leakage rate q of the horizontal segment after the ith superpositionti(i-1, 2,3, …, k) is equal to the engineering allowed loss rate qt]If q isti≠[qt]Returning to the third step to calculate the drilling fluid density rho after the i +1 th superpositioni+1Repeating the fourth step to the tenth step; if q isti＝[qt]Determining the bottom hole pressure P after the ith superposition at the momentLiCorresponding leakage pressure P for the calculated pointfAnd ending the calculation.
2. The method of claim 1, wherein the method comprises: and in the second step, the annular space and the drilling fluid in the fracture belong to yield power law fluid.
3. The method of claim 1, wherein the method comprises: the value range of the drilling fluid density superposition value delta rho is 0.01-0.05 g/cm3。
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