CN111502639B - Method for determining minimum well killing displacement of relief well - Google Patents
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Abstract
The invention relates to a method for determining minimum well killing displacement of a relief well, which is used for determining a well killing construction selection parameter range of the relief well according to the maximum well killing liquid density and the rated displacement of a well killing pump which can be prepared in the present place and by combining a minimum well killing displacement relation curve; and selecting proper well control fluid density and displacement from the parameter range according to the field equipment capacity and personnel equipment, preparing a well control pump and weighting drilling fluid, and implementing well control. The invention utilizes the established multiphase flow control equation set to calculate the minimum well control displacement required by different well control liquid densities, and determines the well control construction parameter selection range according to the maximum well control liquid density and the rated displacement of the well control pump which can be prepared in the present place, thereby providing guidance for the on-site well control construction parameter design; the multiphase flow control equation set considers the falling of the well control fluid at the connecting points, and solves the equation set by adopting a fully implicit four-point differential algorithm and combining a non-uniform grid division method, so that the calculation accuracy is improved.
Description
Technical Field
The invention belongs to the technical field of unconventional well control, and particularly relates to a method for determining minimum well control displacement of a relief well.
Background
The oil gas resource is an important strategic energy source, and has immeasurable effect in the aspect of protecting national economic and social development and national defense safety. However, oil and gas exploitation is a high-risk work, and once blowout accidents occur, not only the resources are lost, equipment is damaged, but also casualties, environmental damage and bad social influence can be caused. The well control technology is an indispensable important component in modern drilling and production engineering, is highly valued, and plays an important role in treating blowout accidents, reducing property loss, reducing environmental pollution and the like.
The relief well is used as an unconventional well control technology, is the last means for treating blowout accidents, can solve serious blowout accidents which cannot be solved by the conventional well control mode, and is an important guarantee for safely and efficiently exploiting oil and gas resources. In particular, after the occurrence of the oil leak in the gulf of mexico in 2010, western oil companies are more demanding complete relief well designs before deep water drilling operations can be performed. The relief well is controlled by dynamic well control, and the principle is that the blowout is prevented by using the liquid column pressure of well control liquid and the flowing friction generated by high displacement. Because the rescue well adopts the principle of magnetic detection to communicate with the accident well, the communication point is not at the bottom of the accident well, but near the last layer of casing shoes, when the open hole section is longer, whether the well control liquid can drop at the communication point and the flowing condition of the open hole section after the drop can have great influence on the design of the well control displacement. Due to the limitation of offshore well control equipment, the minimum well control displacement required by successful well control is required to be calculated before construction so as to ensure that the selected construction displacement can successfully stop blowout, reduce the waste of well control liquid and reduce the pollution to the environment, and therefore, the determination of the minimum well control displacement of the relief well is of great importance.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides a method for determining the minimum well killing displacement of a relief well; calculating the minimum well control displacement required by different well control fluid densities by establishing a multiphase flow control equation set considering the falling of the well control fluid at the connecting point, drawing a relation curve of the well control fluid density and the minimum well control displacement, and then determining the well control construction parameters of the relief well according to the maximum well control fluid density and the rated displacement of the well control pump which can be prepared in the field. By the method, the minimum well control displacement of the relief well can be determined, and guidance is provided for the design of the well control construction parameters of the relief well.
The invention provides a method for determining minimum well killing displacement of a relief well, which comprises the following steps:
(1) Determining basic parameters required by minimum well control displacement calculation of the relief well;
(2) Dispersing the shaft length and the well killing time of the accident well into grids according to a space domain and a time domain respectively;
(3) Taking the falling of the well control fluid at the communication point into consideration, and establishing a multiphase flow control equation set of the well bore in the well control process;
(4) Determining initial conditions, boundary conditions and solving algorithms of the multiphase flow equation set by combining the basic parameters in the step (1) and the multiphase flow control equation set in the step (3);
(5) Calculating the minimum well control displacement required under different well control liquid densities by combining the grid division in the step (2) and the equation set in the step (3), and drawing a relation curve of the well control liquid density and the minimum well control displacement;
(6) And determining the minimum well killing displacement of the relief well according to the relation curve between the maximum well killing liquid density which can be prepared in the present place and the step 5.
Wherein, the basic parameters in the step (1) include: accident well depth H t Naked eye segment length H o Length H of casing section c Formation pressure P p Formation temperature T f Gas production index PI, wellhead back pressure P wh Viscosity mu of well killing liquid l Gas composition, casing roughness, initial bottom hole flow pressure P wf0 And initial gas yield Q g0 。
The specific method in the step (2) is as follows: the space domain starts from the bottom of the well to the end of the well mouth, space grids are divided by adopting 'up-close and down-open', the density of the upper grid of the well shaft is high, the density of the lower grid of the well shaft is small, space nodes are respectively 1, 2, 3 and M, wherein M is the total number of the space nodes, and M is determined according to the set single longest operation time; the time domain starts from the beginning of injection of the well control fluid into the accident well until the gas-liquid two-phase flow interface reaches the wellhead, the time grid length is determined according to the space grid length and the gas ascending speed, and the time nodes are respectively 1, 2, 3, & N and N, wherein N is the total number of the time nodes.
The wellbore multiphase flow control equation set in the step (3) comprises a continuity equation, a momentum equation and an auxiliary equation, wherein the auxiliary equation mainly comprises: critical gas velocity equations, interfacial shear force equations, interphase interface contact length equations, gas PVT equations, gas yield equations, flow pattern discrimination equations, and formation temperature field equations.
Wherein the continuity equation is:
and (3) production section:
non-production section:
wherein A is the cross-sectional area of the shaft, m 2 ；E g Is void ratio and dimensionless; ρ g Is of gas density, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the s is a coordinate along the flow direction, m; t is time, s; v g Is the gas velocity, m/s; g g The gas production quality per unit time and unit thickness is kg/(m.s); e (E) l Is the liquid holdup and is dimensionless; ρ l Is of liquid density, kg/m 3 ；v l Liquid velocity, m/s;
the momentum equation is:
natural gas:
well killing liquid:
wherein g is gravity acceleration, m/s 2 ；τ gl Is gas-liquid interface shearing force, pa; s is S gl The gas-liquid contact length is m; τ wg Pa is the interfacial shear force between the gas and the pipe wall; s is S wg The contact length of the gas and the pipe wall is m; τ wl Pa is the interfacial shear force between the liquid and the pipe wall; s is S wl The contact length between the liquid and the pipe wall is m; the + -represents that positive is taken when the liquid film movement direction is the same as s, and negative is taken when the liquid film movement direction is opposite to s;
in the auxiliary equation:
critical gas velocity equation: v cg ＝f(ρ m ,ρ g ,v m ,v g ,D) (6)
Interphase interface contact length equation: s=f (σ, v m ,v g ,D，k) (7)
Interfacial shear force equation：τ＝(v m ,v g ,D,μ l ，μ g ，k) (8)
Gas PVT equation: ρ g ＝f(P,T) (9)
Gas production speed equation: q (Q) g ＝f(P p ,P wf ,PI) (10)
Flow pattern discrimination equation: fp=f (P, T, v m ，v g ，E g ，ρ m ,ρ g ,D，σ) (11)
Formation temperature field equation: t (T) f ＝(T 0 ,H t ,△T) (12)
Wherein sigma is surface tension, N/m; d is the diameter of the well, m; k represents different phase contacts, dimensionless; mu (mu) l Is the viscosity of liquid, pa.s; mu (mu) g Is the gas viscosity, pa.s; p is pressure, pa; t is the temperature, K; p (P) p Is the formation pressure, pa; p (P) wf Is bottom hole pressure, pa; PI is the gas production index, m 3 /(d·MPa)；T 0 The formation temperature, K; h t The well depth is m of an accident well; delta T is the ground temperature gradient, K/m.
Wherein, in the step (4):
(41) Determination of initial conditions:
before the start of the kill operation, the accident well bore is a single phase gas flow; the initial conditions may be determined from the Inflow (IPR) and outflow (OPR, Q) of the gas well m =0) determination;
bottom hole flow pressure P wf Gas production rate Q of gas well g The initial conditions of (2) are:
P wf (0)＝P wf0 (13)
Q g (0)＝Q g0 (14)
wherein P is wf0 And Q g0 The unit is Pa and m respectively the bottom hole flow pressure and the gas production speed when no-pressure well fluid is injected 3 /s；
(42) Boundary condition determination:
the boundary conditions of the gas production rate are:
Q g (H t ,t)＝Q g (15)
the boundary conditions for pressure are:
P c (H c ,t)＝P o (0,t) (16)
P o (H o ,t)＝P wf (17)
wherein H is c Length of the sleeve section, m; h o The length of the naked eye section is m; subscripts c and o represent the casing section and the open hole section, respectively;
(43) Solving algorithm: and solving a multiphase flow equation by adopting a fully implicit four-point differential method.
Wherein, the step (5) comprises the following steps:
(51) Determining a calculation method of minimum well killing displacement required under a certain well killing liquid density;
(52) Calculating minimum well killing displacement required under different well killing liquid densities;
(53) And drawing a relation curve of the density of the well control fluid and the minimum well control displacement in a coordinate system.
The calculation method of the minimum well killing displacement required by the certain well killing liquid density in the step (51) comprises the following steps:
(511) Inputting a density ρ of the well control fluid m ；
(512) Estimating minimum well control displacement Q required under the density of the well control liquid m ；
(513) Assuming time node 1 moment and bottom hole pressure P wf1 ；
(514) Calculating a critical gas velocity using formula (6), and calculating a gas production velocity using formula (10);
(515) Judging whether well killing liquid falls at the connecting point: if the gas speed is smaller than the critical gas speed, the well control liquid falls, and the open hole section calculates pressure drop according to the gas-liquid two-phase flow; otherwise, the naked eye section calculates the pressure drop according to the single-phase airflow; taking gas-liquid two-phase flow as an example, assume that the pressure drop of two nodes i and i+1 isCalculating node pressure drop using formula (5)>If the difference between the two meets the precision requirement, stopping calculating the node i, and calculating the node i+1 by taking each parameter at the i as a known condition; otherwise, the node voltage drop is re-assumed until the precision requirement is met;
(516) Calculating the pressure of each space node of the casing section;
(517) Judging whether the difference between the calculated value and the assumed value of the wellhead pressure meets the precision requirement, and if so, indicating that the assumed value of the bottom hole pressure is reasonable; otherwise, returning to the step (513) until the precision requirement is met;
(518) Calculating the moment n when the well control liquid reaches the wellhead by utilizing a continuity equation of the well control liquid;
(519) Judging whether the bottom hole pressure at the moment n is larger than the formation pressure, and the difference between the bottom hole pressure and the formation pressure meets the precision requirement: if so, explain Q m Is the density rho of the well control fluid m Minimum kill displacement required; otherwise, return to step (512) until the requirements are met.
Wherein, in the step (52): according to the calculation method in the step (51), the density of the well control fluid is calculated as rho m1 ，ρ m2 ，ρ m3 ，···，ρ mK Minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK 。
Wherein, in the step (53): at the density ρ of the well control fluid m1 ，ρ m2 ，ρ m3 ，···，ρ mK As independent variable, minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK And drawing a relation curve between the two in a coordinate system as a dependent variable to obtain a relation curve of the density of the well control fluid and the minimum well control displacement.
The application of the method for determining the minimum well killing displacement of the relief well in the field well killing construction is also within the protection scope of the invention, for example, the range of the selected parameter of the relief well killing construction is determined according to the maximum well killing liquid density and the rated displacement of a well killing pump which can be prepared in the field and by combining a minimum well killing displacement relation curve; and selecting proper well control fluid density and displacement from the parameter range according to the field equipment capacity and personnel equipment, preparing a well control pump and weighting drilling fluid, and implementing well control.
Compared with the prior art, the invention has the following beneficial effects:
(1) Calculating the minimum well control displacement required by different well control fluid densities by using the established multiphase flow control equation set, and determining a well control construction parameter selection range according to the maximum well control fluid density and the rated displacement of a well control pump which can be prepared in the present place, so as to provide guidance for the on-site well control construction parameter design;
(2) The multiphase flow control equation set considers the falling of the well control fluid at the connecting points, and solves the equation set by adopting a fully implicit four-point differential algorithm and combining a non-uniform grid division method, so that the calculation accuracy is improved.
Drawings
FIG. 1 is a schematic illustration of a rescue well communicating with an accident well;
FIG. 2 is a flow chart of a method of determining minimum kill displacement for a relief well;
FIG. 3 is a flow chart of a calculation to determine a minimum kill rate required for a given kill fluid density;
FIG. 4 is a graph of the relationship between the density of different well control fluids and the minimum well control displacement, and the range of values of the well control parameters.
Detailed Description
As shown in fig. 1, the relief well is a directional well, and is usually communicated with the accident well by adopting the principle of magnetic detection, the communication point is near the last layer of casing shoes of the accident well, the casing section is arranged above the communication point, and the open hole section is arranged below the communication point. The relief well is controlled by dynamic well control, and the principle is that the blowout is prevented by using the liquid column pressure of well control liquid and the flowing friction generated by high displacement. Whether the well control fluid falls at the communication point or not and the flowing condition of the open hole section after the well control fluid falls can have a great influence on the design of the well control displacement. Due to the limitation of offshore well control equipment, the minimum well control displacement required by successful well control is required to be calculated before construction so as to ensure that the selected construction displacement can successfully stop blowout, reduce the waste of well control liquid and reduce the pollution to the environment, and therefore, the determination of the minimum well control displacement of the relief well is of great importance.
The method for determining the minimum well killing displacement of the relief well is shown in fig. 2, and comprises the following steps:
1. basic parameters required by minimum well control displacement calculation of relief well are determined
The basic parameters mainly comprise: accident well depth H t Naked eye segment length H o Length H of casing section c Formation pressure P p Formation temperature T f Gas production index PI, wellhead back pressure P wh Viscosity mu of well killing liquid l Gas composition, casing roughness, initial bottom hole flow pressure P wf0 Initial gas yield Q g0 。
2. Discretizing the length of the accident well shaft and the well control time into grids
The space domain starts from the bottom of the well to the end of the well mouth, space grids are divided by adopting 'up-close-down-open', the density of the upper grid of the well shaft is high, the density of the lower grid is small, space nodes are respectively 1, 2, 3, M and M, wherein M is the total number of space nodes, M can be determined according to the set space step length and well depth, for example, L is well depth M, delta L is unit step length can be 1M, and at the moment, M=L/delta L; the time domain starts from the beginning of injection of the well control fluid into the accident well until the gas-liquid two-phase flow interface reaches the well head, the time grid length is determined according to the space grid length and the gas ascending speed, the time network length δt=δl/VG, VG being the gas velocity, the time node being denoted by j, respectively 1, 2, 3, & gtN, wherein N is the total number of time nodes.
3. Establishing a multiphase flow control equation set considering the drop of the well control fluid at the communication point
Taking the falling of well control fluid at a communication point into consideration, establishing a wellbore multiphase flow control equation set in the well control process, wherein the wellbore multiphase flow control equation set comprises a continuity equation, a momentum equation and an auxiliary equation, and the auxiliary equation mainly comprises: critical gas velocity equation, interfacial shear force equation, interphase interface contact length equation, gas PVT equation, gas yield equation, flow pattern discrimination equation, formation temperature field equation.
(1) Continuity equation:
and (3) production section:
non-production section:
wherein A is the cross-sectional area of the shaft, m 2 ；E g Is void ratio and dimensionless; ρ g Is of gas density, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the s is a coordinate along the flow direction, m; t is time, s; v g Is the gas velocity, m/s; g g The gas production quality per unit time and unit thickness is kg/(m.s); e (E) l Is the liquid holdup and is dimensionless; ρ l Is of liquid density, kg/m 3 ；v l Liquid velocity, m/s.
(2) Momentum equation:
natural gas:
well killing liquid:
wherein g is gravity acceleration, m/s 2 ；τ gl Is gas-liquid interface shearing force, pa; s is S gl The gas-liquid contact length is m; τ wg Pa is the interfacial shear force between the gas and the pipe wall; s is S wg The contact length of the gas and the pipe wall is m; τ wl Pa is the interfacial shear force between the liquid and the pipe wall; s is S wl The contact length between the liquid and the pipe wall is m; + -means when the liquid film movesThe direction is positive when s is the same, and negative when s is the opposite direction.
(3) Auxiliary equation
Critical gas velocity equation: v cg ＝f(ρ m ,ρ g ,v m ,v g ,D) (6)
Interphase interface contact length equation: s=f (σ, v m ,v g ,D，k) (7)
Interfacial shear force equation: τ= (v) m ,v g ,D,μ l ，μ g ，k) (8)
Gas PVT equation: ρ g ＝f(P,T) (9)
Gas production speed equation: q (Q) g ＝f(P p ,P wf ,PI) (10)
Flow pattern discrimination equation: fp=f (P, T, v m ，v g ，E g ，ρ m ,ρ g ,D，σ) (11)
Formation temperature field equation: t (T) f ＝(T 0 ,H t ,△T) (12)
Wherein sigma is surface tension, N/m; d is the diameter of the well, m; k represents different phase contacts, dimensionless; mu (mu) l Is the viscosity of liquid, pa.s; mu (mu) g Is the gas viscosity, pa.s; p is pressure, pa; t is the temperature, K; p (P) p Is the formation pressure, pa; p (P) wf Is bottom hole pressure, pa; PI is the gas production index, m 3 /(d·MPa)；T 0 The formation temperature, K; h t The well depth is m of an accident well; delta T is the ground temperature gradient, K/m.
4. Determining initial conditions, boundary conditions and solving algorithms for a multi-phase flow equation set
(1) Initial conditions
Before the start of the kill operation, the accident well bore is a single phase gas stream. The initial conditions may be determined from the Inflow (IPR) and outflow (OPR, Q) of the gas well m =0) determination.
Bottom hole flow pressure P wf Gas production rate Q of gas well g The initial conditions of (2) are:
P wf (0)＝P wf0 (13)
Q g (0)＝Q g0 (14)
wherein P is wf0 And Q g0 The unit is Pa and m respectively the bottom hole flow pressure and the gas production speed when no-pressure well fluid is injected 3 /s。
(2) Boundary conditions
The boundary conditions of the gas production rate are:
Q g (H t ,t)＝Q g (15)
the boundary conditions for pressure are:
P c (H c ,t)＝P o (0,t) (16)
P o (H o ,t)＝P wf (17)
wherein H is c Length of the sleeve section, m; h o The length of the naked eye section is m; subscripts c and o represent the casing segment and the open hole segment, respectively.
(3) Solution algorithm
And solving a multiphase flow equation by adopting a fully implicit four-point differential method.
5. The minimum well control displacement required under a certain well control liquid density is calculated, as shown in fig. 3, and the specific steps are as follows:
(1) Determining a fluid density ρ m ；
(2) Estimating the minimum well control displacement Q required under the well control liquid density determined in the step (1) m The method comprises the steps of carrying out a first treatment on the surface of the The estimation can be based on the previous drilling fluid displacement, or the conventional engineering or driller's law well-killing displacement, and the value is just an initial value and does not influence the final calculation result.
(3) Assuming time node 1 moment and bottom hole pressure P wf1 ；
(4) Calculating a critical gas velocity using formula (6), and calculating a gas production velocity using formula (10);
(5) Judging whether well killing liquid falls at the connecting point: if the gas speed is smaller than the critical gas speed, the well control liquid falls, and the open hole section calculates pressure drop according to the gas-liquid two-phase flow; otherwise, the naked eye section calculates the pressure drop according to the single-phase airflow; taking gas-liquid two-phase flow as an example, two spatial nodes are assumedThe pressure drop between points i and i+1 isCalculating node pressure drop using formula (5)>If the difference between the two meets the precision requirement, stopping calculating the node i, and calculating the node i+1 by taking each parameter at the i as a known condition; otherwise, the node voltage drop is re-assumed until the precision requirement is met; (wherein the accuracy requirement is a range set according to the requirement in the specific implementation)
(6) Calculating the pressure of each space node of the casing section;
(7) Judging whether the difference between the calculated value and the assumed value of the wellhead pressure meets the precision requirement, and if so, indicating that the assumed value of the bottom hole pressure is reasonable; otherwise, returning to the step (3) until the precision requirement is met;
(8) Calculating the moment n when the well control liquid reaches the wellhead by utilizing a continuity equation of the well control liquid; and n is an intermediate variable, which means that in discrete space coordinates, after a plurality of steps of iterative computation, the well control fluid reaches a well head node, and the iterative step number is calculated as n.
(9) Judging whether the bottom hole pressure at the moment n is larger than the formation pressure, and the difference between the bottom hole pressure and the formation pressure meets the precision requirement: if so, explain Q m Is the density rho of the well control fluid m Minimum kill displacement required; otherwise, returning to the step (2) until the requirement is met.
6. Calculating minimum well control displacement required under different well control liquid densities
According to the calculation flow of the step 5, the density of the well control fluid is calculated as ρ m1 ，ρ m2 ，ρ m3 ，···，ρ mK Minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK 。
7. Drawing a relation graph of well control liquid density and minimum well control displacement in a coordinate system
At the density ρ of the well control fluid m1 ，ρ m2 ，ρ m3 ，···，ρ mK As independent variable, minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK And drawing a relation curve between the two as a dependent variable to obtain a relation curve of the density of the well control fluid and the minimum well control displacement.
8. And obtaining the minimum well killing displacement according to the maximum well killing liquid density which can be prepared in the present place and the relation curve.
In addition, during specific construction, according to the maximum well control liquid density and the rated displacement of a well control pump which can be prepared at the present place, and in combination with the minimum well control displacement relation curve, the well control construction selection parameter range of the relief well is determined, as shown in the shaded part of fig. 4. Depending on field device capabilities and personnel equipment, appropriate kill fluid densities and displacements are selected from the shaded area of FIG. 4, and the kill pump and weighted drilling fluid are prepared to implement the kill.
Modifications and variations of the above embodiments will be apparent to those skilled in the art in light of the above teachings. Therefore, the invention is not limited to the specific embodiments disclosed and described above, but some modifications and changes of the invention should be also included in the scope of the claims of the invention. In addition, although specific terms are used in the present specification, these terms are for convenience of description only and do not limit the present invention in any way.
Claims (3)
1. A method for determining minimum well killing displacement of a relief well is characterized by comprising the following steps:
(1) Determining basic parameters required by minimum well control displacement calculation of the relief well; the basic parameters include: accident well depth H t Naked eye segment length H o Length H of casing section c Formation pressure P p Formation temperature T f Gas production index PI, wellhead back pressure P wh Viscosity mu of well killing liquid l Gas composition, casing roughness, initial bottom hole flow pressure P wf0 And initial gas yield Q g0 ；
(2) Dispersing the shaft length and the well killing time of the accident well into grids according to a space domain and a time domain respectively;
(3) Taking the falling of the well control fluid at the communication point into consideration, and establishing a multiphase flow control equation set of the well bore in the well control process; the multiphase flow control equation set comprises a continuity equation, a momentum equation and an auxiliary equation, wherein the auxiliary equation mainly comprises: critical gas velocity equation, interfacial shear force equation, interphase interface contact length equation, gas PVT equation, gas production velocity equation, flow pattern discrimination equation and formation temperature field equation;
the continuity equation is:
and (3) production section:
non-production section:
wherein A is the cross-sectional area of the shaft, m 2 ；E g Is void ratio and dimensionless; ρ g Is of gas density, kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the s is a coordinate along the flow direction, m; t is time, s; v g Is the gas velocity, m/s; g g The gas production quality per unit time and unit thickness is kg/(m.s); e (E) l Is the liquid holdup and is dimensionless; ρ l Is of liquid density, kg/m 3 ；v l Liquid velocity, m/s;
the momentum equation includes:
natural gas:
well killing liquid:
wherein g is gravity acceleration, m/s 2 ；τ gl Is gas-liquid interface shearing force, pa; s is S gl The gas-liquid contact length is m; τ wg Pa is the interfacial shear force between the gas and the pipe wall; s is S wg The contact length of the gas and the pipe wall is m; τ wl Pa is the interfacial shear force between the liquid and the pipe wall; s is S wl The contact length between the liquid and the pipe wall is m; the + -represents that positive is taken when the liquid film movement direction is the same as s, and negative is taken when the liquid film movement direction is opposite to s;
the auxiliary equation includes:
critical gas velocity equation: v cg ＝f(ρ m ,ρ g ,v m ,v g ,D) (6)
Interphase interface contact length equation: s=f (σ, v m ,v g ,D，k) (7)
Interfacial shear force equation: τ= (v) m ,v g ,D,μ l ，μ g ，k) (8)
Gas PVT equation: ρ g ＝f(P,T) (9)
Gas production speed equation: q (Q) g ＝f(P p ,P wf ,PI) (10)
Flow pattern discrimination equation: fp=f (P, T, v m ，v g ，E g ，ρ m ,ρ g ,D，σ) (11)
Formation temperature field equation: t (T) f ＝(T 0 ,H t ,△T) (12)
Wherein ρ is m To the density of the well control liquid, kg/m 3 ；V m Is the well killing liquid speed, m/s; sigma is surface tension, N/m; d is the diameter of the well, m; k represents different phase contacts, dimensionless; mu (mu) l Is the viscosity of liquid, pa.s; mu (mu) g Is the gas viscosity, pa.s; p is pressure, pa; t is the temperature, K; p (P) p Is the formation pressure, pa; p (P) wf Is bottom hole pressure, pa; PI is the gas production index, m 3 /(d·MPa)；T 0 The formation temperature, K; h t For thingsSo the well depth, m; delta T is the ground temperature gradient, K/m;
(4) Determining initial conditions, boundary conditions and solving algorithms of the multiphase flow equation set by combining the basic parameters in the step (1) and the multiphase flow control equation set in the step (3);
(41) Determination of initial conditions:
before the start of the kill operation, the accident well bore is a single phase gas flow; the initial conditions may be determined from gas well inflow and outflow profiles;
bottom hole flow pressure P wf Gas production rate Q of gas well g The initial conditions of (2) are:
P wf (0)＝P wf0 (13)
Q g (0)＝Q g0 (14)
wherein P is wf0 And Q g0 The unit is Pa and m respectively the bottom hole flow pressure and the gas production speed when no-pressure well fluid is injected 3 /s；
(42) Boundary condition determination:
the boundary conditions of the gas production rate are:
Q g (H t ,t)＝Q g (15)
the boundary conditions for pressure are:
P c (H c ,t)＝P o (0,t) (16)
P o (H o ,t)＝P wf (17)
wherein H is c Length of the sleeve section, m; h o The length of the naked eye section is m; subscripts c and o represent the casing section and the open hole section, respectively;
(43) Solving algorithm: solving a multiphase flow equation by adopting a fully implicit four-point differential method;
(5) Calculating the minimum well control displacement required under different well control liquid densities by combining the grid division in the step (2) and the equation set in the step (3), and drawing a relation curve of the well control liquid density and the minimum well control displacement;
(6) Determining minimum well killing displacement of the relief well according to the maximum well killing liquid density which can be prepared in the present place and the relation curve in the step (5);
the specific method in the step (2) is as follows: the space domain starts from the bottom of the well to the end of the well mouth, space grids are divided by adopting 'up-close and down-open', the density of the upper grid of the well shaft is high, the density of the lower grid of the well shaft is small, space nodes are respectively 1, 2, 3 and M, wherein M is the total number of the space nodes, and M is determined according to the set single longest operation time; the time domain starts from the beginning of injection of the well control fluid into the accident well until the gas-liquid two-phase flow interface reaches the wellhead, the time grid length is determined according to the space grid length and the gas ascending speed, and the time nodes are respectively 1, 2, 3, & N, and N is the total number of the time nodes;
the step (5) comprises the following steps:
(51) Determining a calculation method of minimum well killing displacement required under a certain well killing liquid density;
(52) Calculating minimum well killing displacement required under different well killing liquid densities;
(53) Drawing a relation curve of the density of the well control fluid and the minimum well control displacement in a coordinate system;
the method for calculating the minimum well control displacement required by the certain well control liquid density in the step (51) comprises the following steps:
(511) Inputting a density ρ of the well control fluid m ；
(512) Estimating minimum well control displacement Q required under the density of the well control liquid m ；
(513) Assuming time node 1 moment and bottom hole pressure P wf1 ；
(514) Calculating a critical gas velocity using formula (6), and calculating a gas production velocity using formula (10);
(515) Judging whether well killing liquid falls at the connecting point: if the gas speed is smaller than the critical gas speed, the well control liquid falls, and the open hole section calculates pressure drop according to the gas-liquid two-phase flow; otherwise, the naked eye section calculates the pressure drop according to the single-phase airflow; taking gas-liquid two-phase flow as an example, assume that the pressure drop of two nodes i and i+1 isCalculating node pressure drop using formula (5)>If the difference between the two meets the precision requirement, stopping calculating the node i, and calculating the node i+1 by taking each parameter at the i as a known condition; otherwise, the node voltage drop is re-assumed until the precision requirement is met;
(516) Calculating the pressure of each space node of the casing section;
(517) Judging whether the difference between the calculated value and the assumed value of the wellhead pressure meets the precision requirement, and if so, indicating that the assumed value of the bottom hole pressure is reasonable; otherwise, returning to the step (513) until the precision requirement is met;
(518) Calculating the moment n when the well control liquid reaches the wellhead by utilizing a continuity equation of the well control liquid;
(519) Judging whether the bottom hole pressure at the moment n is larger than the formation pressure, and the difference between the bottom hole pressure and the formation pressure meets the precision requirement: if so, explain Q m Is the density rho of the well control fluid m Minimum kill displacement required; otherwise, return to step (512) until the requirements are met.
2. The method of determining minimum well killing displacement for a relief well according to claim 1, wherein in step (52): according to the calculation method in the step (51), the density of the well control fluid is calculated as rho m1 ，ρ m2 ，ρ m3 ，···，ρ mK Minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK The method comprises the steps of carrying out a first treatment on the surface of the In step (53): at the density ρ of the well control fluid m1 ，ρ m2 ，ρ m3 ，···，ρ mK As independent variable, minimum well control displacement Q m1 ，Q m2 ，Q m3 ，···，Q mK And drawing a relation curve between the two in a coordinate system as a dependent variable to obtain a relation curve of the density of the well control fluid and the minimum well control displacement.
3. The method for determining minimum well killing displacement of a relief well according to claim 1 or 2, applied to the field of well killing construction of relief wells.
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| CN114841088B (en) * | 2022-04-23 | 2024-09-24 | 西南石油大学 | Direct-pushing well killing minimum displacement calculation method considering gas-liquid countercurrent |
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