CN118246358A - Deep drilling overflow state sensing method based on extended Kalman filtering prediction - Google Patents
Deep drilling overflow state sensing method based on extended Kalman filtering prediction Download PDFInfo
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Abstract
The invention relates to a deep well drilling overflow and leakage state sensing method based on extended Kalman filtering prediction, which belongs to the technical field of well drilling control and comprises the steps of establishing a well drilling shaft and stratum coupling flow system state space model based on a bonding diagram principle; establishing an observation equation model of a state space model of a coupling flow system of the drilling shaft and the stratum by utilizing real-time data of logging parameters such as pressure, inlet and outlet flow, slurry pond increment and the like before and after overflow occurs; establishing a state equation model of a state space model of a well drilling shaft and stratum coupling flow system by using a pore medium seepage theory and an oil and gas well fluid mechanics principle; and predicting the formation pressure and the coupling flow state of the shaft and the stratum in real time by introducing an extended Kalman filtering prediction method. The invention can reduce the false alarm rate of the system while finding out underground spills in advance, effectively reduce the well kick risk of drilling in abnormal high-pressure stratum, avoid well blowout accidents and provide safety guarantee for subsequent drilling operation.
Description
Technical Field
The invention relates to a deep well drilling overflow and leakage state sensing method based on extended Kalman filtering prediction, and belongs to the technical field of well drilling control.
Background
With the development of economy, the demand of China for oil and gas resources is also continuously increased, but as the early dominant oil field mostly enters the middle and later stages of development, the crude oil yield is difficult to break through greatly, so that the dependence of the oil and gas in China on the external environment is high in recent years. Therefore, the oil and gas exploration and development of China gradually progress to deep complex stratum. However, deep formations face a number of complex geological problems, which can lead to risks in drilling construction due to the inability of existing geophysical methods to accurately predict formation pressure, such as: in deep ultra-deep well drilling in the western region of China, strata with narrow pressure windows are frequently encountered, and underground anomalies such as kick, lost circulation and the like frequently occur when drilling according to an initial drilling scheme. If the well is not found timely, complex systematic risks such as blowout, malignant return and the like are likely to be caused, and serious malignant accidents such as well destruction and death are caused. Advanced monitoring and control equipment is often used for this purpose, for example conventional pressure control equipment is provided on low risk wells, and fine pressure control equipment with advanced downhole measuring instruments is provided on high risk or key wells, which equipment in use well ensures well drilling safety. However, with the increasing of the drilling depth, the high-temperature environment of the deep stratum causes that the underground fine pressure measuring instrument cannot be used, so that the underground fine pressure measuring instrument can only rely on conventional ground pressure control drilling equipment on high-risk and key wells, and because the pressure information at the bottom of the well can not be acquired, when overflow or lost circulation occurs, on-site personnel cannot find the underground overflow and lost circulation state in time, so that the well is not closed timely, the well closing casing pressure is higher, and the well control risk is larger.
On the other hand, under the existing conventional pressure-controlled drilling technical framework, well kick and lost circulation monitoring is carried out by adopting abnormal change based on a certain parameter, for example, a special person is arranged to observe the volume of a mud pit. However, when the kick and the lost circulation occur, abnormal changes occur at the same time due to the existence of multiple parameters, and the changes have internal relations, so that the characteristics of multi-parameter cooperative response are realized, and therefore, a system modeling method is needed to realize the monitoring of the overflow and lost circulation state. Under the guidance of a new theoretical method, the technology of multi-source information fusion is adopted to realize the technology of timely forecasting the underground overflow information based on the ground logging data, so that a series of well control risks caused by overflow monitoring delay are avoided.
Disclosure of Invention
In order to solve the defects of the prior art, the method for early identifying the underground overflow state of deep well ultra-deep well drilling is implemented by utilizing the conventional pressure control drilling technology, so that the system false alarm rate can be reduced while the underground overflow is found in advance, the well kick risk of drilling in an abnormally high pressure stratum is effectively reduced, the well blow accident is avoided, and the safety guarantee is provided for subsequent drilling operation.
The invention adopts the following technical scheme:
a deep well drilling overflow state sensing method based on extended Kalman filtering prediction comprises the following steps:
s1: establishing a state space model of a well drilling shaft and stratum coupling flow system based on a bonding diagram principle;
S2: an observation equation model of a state space model of a coupling flow system of the drilling shaft and the stratum is established by utilizing real-time data of logging parameters such as pressure before and after overflow occurs (vertical pressure is adopted in drilling circulation working conditions, casing pressure is adopted in non-drilling circulation working conditions), inlet and outlet flow, increment of a mud pit and the like;
s3: establishing a state equation model of a state space model of a well drilling shaft and stratum coupling flow system by using a pore medium seepage theory and an oil and gas well fluid mechanics principle;
s4: and the formation pressure (pore and leakage) and the coupling flow state of the shaft and the stratum are predicted in real time by introducing an extended Kalman filtering prediction method.
Preferably, in step S1, the method for establishing the state space model of the coupling flow system between the well drilling shaft and the stratum based on the bond map principle is as follows:
In a well bore and formation coupled flow system state space model, a pump flow source of known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; elements like mud tanks (e.g. mud tanks) are modeled as capacitive elements C; the liquid filled conduit is denoted by inertial element I and the fluid friction and thus the pressure drop is denoted by resistive element R; mass conservation is modeled by a common potential junction 0 node, and momentum conservation is modeled by a common current junction 1 node;
the state space model of the coupling flow system of the drilling well shaft and the stratum can be divided into a state space model of the coupling flow system of the drilling well shaft and the stratum during a drilling cycle and a state space model of the coupling flow system of the drilling well shaft and the stratum during a non-drilling cycle according to different working conditions;
the bond map composition of the borehole and formation coupled flow system state space model during the drilling cycle is as follows:
Defining a drilling fluid conveying channel from a drilling pump to a bottom of a well, wherein the drilling fluid conveying channel comprises a ground pipeline, a drill string and a drill bit water hole which are 1# concurrent junctions 1 (left); defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 2# co-flow junction 1 (right); defining 3# co-current junction 1 (lower) from reservoir to annulus; defining a well bottom coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward movement as a 1# common potential junction 0;
in a 1# co-flow junction 1 of a drilling fluid conveying channel from a drilling pump to a well bottom, a resistive element comprises a pressure drop coefficient Rrd in a drill rod and a bit partial pressure drop coefficient Rdb, and the pressure drop coefficient Rd and the bit partial pressure drop coefficient Rdb correspond to a drill string circulation pressure loss Prd and a bit partial pressure drop Pdb respectively; the inertia element comprises the inertia Id of drilling fluid in the drill rod, and corresponds to the change rate of the momentum of the drilling fluid in the drill rod The potential source comprises potential source Se of a drilling fluid column in the drill rod, and corresponds to the pressure Pdh of the drilling fluid column in the drill rod; the flow source comprises a pump pressure and displacement flow source Sf of the drilling pump and a flow source Sf flowing out of the drill bit water hole, the pump pressure and displacement flow source Sf of the drilling pump corresponds to the pump pressure Pp and the flow Qp in the drill rod, and the flow source Sf flowing out of the drill bit water hole corresponds to the bottom hole pressure Pbh and the flow Qp in the drill rod;
in the 2# co-current junction 1 of the annulus from the bottom of the annulus to the surface drilling fluid outlet, the potential source comprises potential source Se of the drilling fluid column in the annulus, and corresponds to the annulus fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 3# co-current junction 1 from the reservoir to the annulus, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the potential source comprises a potential source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 1# common potential junction 0, the flow source comprises a flow source Sf flowing out of the water hole of the drill bit, a flow source Sf at the bottom of the annulus and a potential source Sf flowing into the bottom of the well;
because the float valve is arranged in the drill rod, the drill rod is not communicated with the annulus during the pump stopping period, and the bonding diagram of the state space model of the coupling flow system of the drilling shaft and the stratum during the non-drilling circulation period comprises the following components:
Defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 4# co-current junction 1; defining a 5# co-current junction 1 from the reservoir to the annulus; defining a bottom hole coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward return as a common potential junction 0;
In the 4# concurrent 1, the potential source comprises potential source Se of an annular drilling fluid column corresponding to annular fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 5# co-current junction 1, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the flow source comprises a flow source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 2# common potential junction 0, the flow source comprises a flow source Sf at the bottom of an annulus and a flow source Sf flowing into the bottom of the well;
and according to the energy flow direction of the bonding diagram material and the law of conservation of the material and the energy, establishing a state space model of a coupling flow system of the drilling well shaft and the stratum.
Preferably, in step S2, the observation equation model includes a pressure observation equation model, a volume observation equation model, and a flow observation equation model;
The pressure observation equation model is used for representing various circulation friction conditions generated by the pump pressure in the process of overcoming the fluid flow in the well bore in the drilling circulation drilling process, such as the internal circulation friction of a drill rod, the pressure drop of a drill bit, the circulation friction of the annulus of the well bore and the like; in situ, the drilling pump pressure is equal to the vertical pressure without considering the circulation friction of the surface pipeline, and an equation of the pumping pressure containing the formation pressure is constructed by considering the influence of the formation pressure on the pumping pressure, namely:
Pfr＝Pf-Pbh
p p＝Pf-Pfr+Pdr-Ph during the drilling cycle
P c＝Pf-Pfr-Pra-Pah during non-drilling cycle
Wherein P p is pump pressure, pa; p f is the formation pressure, pa; p fr is the pressure differential of the formation pressure and the bottom hole pressure, pa; p bh is bottom hole pressure, pa; p dr is the fluid flow friction resistance in the wellbore drill pipe, pa; p h is the hydrostatic column pressure in the wellbore drill pipe, pa, P c is the casing pressure, pa; p ra is annular circulating pressure consumption, pa; p ah is the annular liquid column pressure, pa.
Preferably, in step S2, the volume observation equation model is used to characterize the volume data of the mud pit observed by the drilling monitoring device, and is affected by errors of the field recording personnel and the monitoring device, and the observation equation model of the volume of the mud pit is as follows:
Vt＝Vm+Vn
wherein V t is the total pool volume of the slurry pool, m 3;Vm is the standard volume of the slurry pool, m 3;Vn is the volume change amount of the slurry pool, and m 3.
Preferably, in step S2, the flow observation equation model is used to represent the relationship between the volume change of the fluid in the well bore annulus, and includes physical parameters such as mass, flow velocity and cross-sectional area, and the physical parameters are related to the well bore annulus momentum physical quantity in the state equation, so as to construct an equation of outlet flow and well bore annulus momentum, where the definition of the well bore annulus inertia coefficient is the mass change rate on a unit area, and considering that the well bore annulus cross-sectional area is different, the well bore annulus is divided into two sections, and an equation is established, which are an open hole section and a casing section (the upper part of the actual well bore is provided with a casing section, and the lower part is provided with no casing is provided with an open hole section):
naked eye section:
Casing section:
Wherein Q o is the fluid flow of the open-hole annulus section, m 3·s-1;Qc is the fluid flow of the open-hole annulus section, m 3·s-1;Γo is the fluid momentum of the open-hole annulus section, kg (m.s) -1;Γc is the fluid momentum of the open-hole annulus section, kg (m.s) -1;;Io is the fluid flow inertia coefficient of the open-hole annulus section, kg.m -4;Ic is the fluid flow inertia coefficient of the open-hole annulus section, and kg.m -4; ρ is the annular fluid density, kg.m -3;Ho is the vertical depth of the open hole section of the annulus, m; h c is the vertical depth of the annular sleeve section, m; a o is the cross-sectional area of an open hole section of the annulus, m 2;Ac is the cross-sectional area of a sleeve section of the annulus, m 2;
In actual monitoring of drilling surface equipment, the subsection fluid flow Q o、Qc of the borehole annulus of the open hole section and the casing section cannot be monitored, but the outlet flow at the wellhead is monitored, and the calculation and integration of the subsection fluid flow are integrated by considering that the characterization parameter in the observation equation is one of drilling parameters and the continuity of flow in the borehole, namely:
Ia＝Io+Ic
Wherein Q a is the outlet flow at the wellhead, m 3·s-1;Γa is the annular fluid momentum, kg· (m·s) -1;Ia is the annular fluid total inertia coefficient, kg·m -4;
the observation equation model is expressed as:
Preferably, the state equation model in step S3 includes: a variation model of pressure difference between a shaft and a stratum, a variation model of annular fluid momentum of the shaft and a variation model of annular fluid mass;
In the variable quantity model of the pressure difference between the well bore and the stratum, the stratum pressure is only related to the depth and does not change along with the drilling time and other parameters, and the change of the stratum pressure along with the depth is random for unpredictable stratum, and the expression is as follows:
In the method, in the process of the invention, Representing the derivative of formation pressure P f with respect to time;
In the well bore annulus fluid momentum change model, according to the conservation of momentum of the fluid in the annulus, and in combination with the well bore-stratum coupling mechanical model, the total momentum change of the annulus drilling fluid is equal to the sum of all forces applied to the fluid at the bottom of the well, and the fluid momentum equation of the well bore annulus is as follows:
In the method, in the process of the invention, Representing the derivative of the annular fluid momentum Γ a with respect to time;
In the annulus fluid mass change model, assuming that the annulus drilling fluid density is constant, the annulus fluid mass change is only related to the volume change of the annulus fluid, and the mass conservation of drilling fluid entering and exiting the mud pit under the normal drilling circulation drilling working condition, namely the volume change of the mud pit is constant; after the kick occurs, stratum fluid invades the shaft, so that the total mass of the fluid in the shaft is increased, the balance of the original drilling fluid in and out is destroyed, and the volume of a mud pit is increased; assuming constant drilling fluid density, the mass change in annulus fluid can be characterized by the fluid reservoir volume change, and the conservation equation is as follows:
In the method, in the process of the invention, The derivative of the volume change V n of the slurry pool with time; q a is the annular outlet flow of the shaft, m 3·s-1;Qp is the inlet flow of the drill pipe, and m 3·s-1;
To sum up, the state equation model can be expressed as:
Preferably, step S4 includes:
s41: linearizing the state equation;
s42: linearizing the observation equation;
s43: discretizing the state equation linearized in the step S41;
S44: and predicting the coupling flow state of the shaft and the stratum in real time by using an extended Kalman filtering prediction method.
Preferably, in steps S41 and S42:
Let state variable x (t) be the change of pressure difference between well bore and stratum, change of annular momentum of well bore and change of annular fluid mass, linearize state equation of state space model of well bore and stratum coupling flow system by Taylor series expansion method, then there are:
f (x) represents a function; delta represents the variation of a certain physical quantity; a 11～a33 is a matrix coefficient after linearization of a state equation;
the observation equation is linearized by the same method, namely, the observation equation of the state space model of the coupling flow system of the well drilling shaft and the stratum is linearized by using the Taylor series expansion method, and the obtained linearization equation is as follows:
Wherein b 11～b33 is a matrix coefficient after linearization of the observation equation.
Preferably, the specific process of step S43 is as follows:
Discretizing the linear state differential matrix by using inverse Laplace variation, namely discretizing the linearized state matrix, wherein the obtained coefficient matrix is marked as A d, and the observation matrix is not a differential equation, so that discretization processing is not needed, and the discretized equation is as follows:
Wherein A d is a state transition matrix, x n is a state change at time n, and x n-1 is a state change at time n-1;
wherein A d＝eAT is a group of the components,
Wherein e is a natural constant, and T is the time interval between data points;
Preferably, the specific process of step S44 is as follows:
(1) Preliminary prediction of state quantity at time n
xn(-)＝Adxn-1(+)
Wherein x n (-) represents the preliminary predicted state quantity at the time of n, and has no dimension; a d represents a state transition matrix; x n-1 (+) is the corrected predicted state quantity at time n-1, dimensionless, x n-1 (+) is a known quantity, and the initial value is the value obtained in the last step, x n (+)Step (1) corresponds to the discretized state matrix equation of fig. 5;
(2) Preliminary prediction of n-moment covariance transfer matrix
Pn(-)＝AdPn-1(+)Ad T+Qn-1
Wherein P n (-) represents the preliminary covariance transfer matrix at time n; p n-1 (+) represents the corrected covariance transfer matrix at time n-1, P n-1 (+) is a known quantity, and the initial value unit matrix is obtained using P n (+) obtained in the previous stepQ n-1 represents a state model error matrix at time n-1;
Wherein the method comprises the steps of G= [ 10 ] T, T represents the matrix transpose; t is the time step of Kalman filtering calculation; /(I)Standard deviation of normal distribution of P f;
(3) Calculating the Kalman gain at time n
Wherein H n is the observation coefficient matrix, i.eR n is the positive variance matrix of the system measurement (observation equation) noise,WhereinStandard deviation of normal distribution of P p,Vt,Qa is determined by accuracy of measurement system;
(4) Correcting and predicting state quantity at n time
xn(+)＝xn(-)+Kn[zn-Hnxn(-)]
Wherein x n (+) is a corrected predicted state quantity at the time of n, and has no dimension; z n is the observed variable at time k, which is
(5) Correction prediction of n-moment covariance transfer torque
Pn(+)＝(I-KnHn)Pn(-)(I-KnHn)T+KnRnKn T
Wherein P n (+) is covariance transfer torque at time n, and I is an identity matrix.
Repeating the steps (1) - (5) with x n(+)、Pn (+) as the previous time parameter, wherein x n (+) of each step is the final prediction resultFrom this variation, the formation pressure P f at this time node, the wellbore annulus hydraulic momentum f a, and the predicted mud Chi Zengliang V n can be found.
The invention is not exhaustive and can be seen in the prior art.
The beneficial effects of the invention are as follows:
The invention can greatly shorten the recognition time after overflow or lost circulation occurs, provide sufficient reaction time for on-site timely well closing, effectively reduce the high-casing pressure risk formed during on-site well closing and well killing, avoid the well kick and blowout risk caused by late overflow discovery, provide more accurate stratum pressure information for subsequent drilling operation, provide technical support for ensuring on-site operation safety, ensure on-site personnel safety and avoid property loss.
The invention can reduce the invasion amount of stratum fluid when overflow is found and reduce the difficulty of subsequent well killing.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application.
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a physical model of wellbore and formation coupled flow state space during a drilling cycle and pump down;
FIG. 3 is a bond diagram of an established wellbore-formation coupled flow state space model of a drilling process;
FIG. 4 is a bond diagram of an established non-drilling cyclic process wellbore and formation coupled flow state space model;
FIG. 5 is a flow chart of extended Kalman filtering prediction for overflow conditions of a wellbore-formation coupled flow system.
Detailed Description
In order to better understand the technical solutions in the present specification, the following description will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the implementation of the present specification, but not limited thereto, and the present invention is not fully described and is according to the conventional technology in the art.
Example 1
An extended Kalman filtering prediction-based deep well drilling overflow state sensing method, as shown in figure 1, comprises the following steps:
s1: establishing a state space model of a well drilling shaft and stratum coupling flow system based on a bonding diagram principle;
S2: an observation equation model of a state space model of a coupling flow system of the drilling shaft and the stratum is established by utilizing real-time data of logging parameters such as pressure before and after overflow occurs (vertical pressure is adopted in drilling circulation working conditions, casing pressure is adopted in non-drilling circulation working conditions), inlet and outlet flow, increment of a mud pit and the like;
s3: establishing a state equation model of a state space model of a well drilling shaft and stratum coupling flow system by using a pore medium seepage theory and an oil and gas well fluid mechanics principle;
S4: and predicting the formation pressure and the coupling flow state of the shaft and the stratum in real time by introducing an extended Kalman filtering prediction method.
Example 2
As described in embodiment 1, except that as shown in fig. 2 to 4, in step S1, a method for establishing a state space model of a well bore and stratum coupling flow system based on a bond map principle is as follows:
In a well bore and formation coupled flow system state space model, a pump flow source of known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; elements like mud tanks (e.g. mud tanks) are modeled as capacitive elements C; the liquid filled conduit is denoted by inertial element I and the fluid friction and thus the pressure drop is denoted by resistive element R; mass conservation is modeled by a common potential junction 0 node, and momentum conservation is modeled by a common current junction 1 node;
the state space model of the coupling flow system of the drilling well shaft and the stratum can be divided into a state space model of the coupling flow system of the drilling well shaft and the stratum during a drilling cycle and a state space model of the coupling flow system of the drilling well shaft and the stratum during a non-drilling cycle according to different working conditions;
the bond map composition of the borehole and formation coupled flow system state space model during the drilling cycle is as follows:
Defining a drilling fluid conveying channel from a drilling pump to a bottom of a well, wherein the drilling fluid conveying channel comprises a ground pipeline, a drill string and a drill bit water hole which are 1# concurrent junctions 1 (left); defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 2# co-flow junction 1 (right); defining 3# co-current junction 1 (lower) from reservoir to annulus; defining a well bottom coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward movement as a 1# common potential junction 0;
in a 1# co-flow junction 1 of a drilling fluid conveying channel from a drilling pump to a well bottom, a resistive element comprises a pressure drop coefficient Rrd in a drill rod and a bit partial pressure drop coefficient Rdb, and the pressure drop coefficient Rd and the bit partial pressure drop coefficient Rdb correspond to a drill string circulation pressure loss Prd and a bit partial pressure drop Pdb respectively; the inertia element comprises the inertia Id of drilling fluid in the drill rod, and corresponds to the change rate of the momentum of the drilling fluid in the drill rod The potential source comprises potential source Se of a drilling fluid column in the drill rod, and corresponds to the pressure Pdh of the drilling fluid column in the drill rod; the flow source comprises a pump pressure and displacement flow source Sf of the drilling pump and a flow source Sf flowing out of the drill bit water hole, the pump pressure and displacement flow source Sf of the drilling pump corresponds to the pump pressure Pp and the flow Qp in the drill rod, and the flow source Sf flowing out of the drill bit water hole corresponds to the bottom hole pressure Pbh and the flow Qp in the drill rod;
in the 2# co-current junction 1 of the annulus from the bottom of the annulus to the surface drilling fluid outlet, the potential source comprises potential source Se of the drilling fluid column in the annulus, and corresponds to the annulus fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 3# co-current junction 1 from the reservoir to the annulus, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the potential source comprises a potential source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 1# common potential junction 0, the flow source comprises a flow source Sf flowing out of the water hole of the drill bit, a flow source Sf at the bottom of the annulus and a potential source Sf flowing into the bottom of the well;
because the float valve is arranged in the drill rod, the drill rod is not communicated with the annulus during the pump stopping period, and the bonding diagram of the state space model of the coupling flow system of the drilling shaft and the stratum during the non-drilling circulation period comprises the following components:
Defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 4# co-current junction 1; defining a 5# co-current junction 1 from the reservoir to the annulus; defining a bottom hole coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward return as a common potential junction 0;
In the 4# concurrent 1, the potential source comprises potential source Se of an annular drilling fluid column corresponding to annular fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 5# co-current junction 1, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the flow source comprises a flow source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 2# common potential junction 0, the flow source comprises a flow source Sf at the bottom of an annulus and a flow source Sf flowing into the bottom of the well;
and according to the energy flow direction of the bonding diagram material and the law of conservation of the material and the energy, establishing a state space model of a coupling flow system of the drilling well shaft and the stratum.
Example 3
As described in embodiment 2, the difference is that in step S2, the observation equation model includes a pressure observation equation model, a volume observation equation model, and a flow observation equation model;
The pressure observation equation model is used for representing various circulation friction conditions generated by the pump pressure in the process of overcoming the fluid flow in the well bore in the drilling circulation drilling process, such as the internal circulation friction of a drill rod, the pressure drop of a drill bit, the circulation friction of the annulus of the well bore and the like; in situ, the drilling pump pressure is equal to the vertical pressure without considering the circulation friction of the surface pipeline, and an equation of the pumping pressure containing the formation pressure is constructed by considering the influence of the formation pressure on the pumping pressure, namely:
Pfr＝Pf-Pbh
p p＝Pf-Pfr+Pdr-Ph during the drilling cycle
P c＝Pf-Pfr-Pra-Pah during non-drilling cycle
Wherein P p is pump pressure, pa; p f is the formation pressure, pa; p fr is the pressure differential of the formation pressure and the bottom hole pressure, pa; p bh is bottom hole pressure, pa; p dr is the fluid flow friction resistance in the wellbore drill pipe, pa; p h is the hydrostatic column pressure in the wellbore drill pipe, pa, P c is the casing pressure, pa; p ra is annular circulating pressure consumption, pa; p ah is the annular liquid column pressure, pa.
Preferably, in step S2, the volume observation equation model is used to characterize the volume data of the mud pit observed by the drilling monitoring device, and is affected by errors of the field recording personnel and the monitoring device, and the observation equation model of the volume of the mud pit is as follows:
Vt＝Vm+Vn
wherein V t is the total pool volume of the slurry pool, m 3;Vm is the standard volume of the slurry pool, m 3;Vn is the volume change amount of the slurry pool, and m 3.
Preferably, in step S2, the flow observation equation model is used to represent the relationship between the volume change of the fluid in the well bore annulus, and includes physical parameters such as mass, flow velocity and cross-sectional area, and the physical parameters are related to the well bore annulus momentum physical quantity in the state equation, so as to construct an equation of outlet flow and well bore annulus momentum, where the definition of the well bore annulus inertia coefficient is the mass change rate on a unit area, and considering that the well bore annulus cross-sectional area is different, the well bore annulus is divided into two sections, and an equation is established, which are an open hole section and a casing section (the upper part of the actual well bore is provided with a casing section, and the lower part is provided with no casing is provided with an open hole section):
naked eye section:
Casing section:
Wherein Q o is the fluid flow of the open-hole annulus section, m 3·s-1;Qc is the fluid flow of the open-hole annulus section, m 3·s-1;Γo is the fluid momentum of the open-hole annulus section, kg (m.s) -1;Γc is the fluid momentum of the open-hole annulus section, kg (m.s) -1;;Io is the fluid flow inertia coefficient of the open-hole annulus section, kg.m -4;Ic is the fluid flow inertia coefficient of the open-hole annulus section, and kg.m -4; ρ is the annular fluid density, kg.m -3;Ho is the vertical depth of the open hole section of the annulus, m; h c is the vertical depth of the annular sleeve section, m; a o is the cross-sectional area of an open hole section of the annulus, m 2;Ac is the cross-sectional area of a sleeve section of the annulus, m 2;
In actual monitoring of drilling surface equipment, the subsection fluid flow Q o、Qc of the borehole annulus of the open hole section and the casing section cannot be monitored, but the outlet flow at the wellhead is monitored, and the calculation and integration of the subsection fluid flow are integrated by considering that the characterization parameter in the observation equation is one of drilling parameters and the continuity of flow in the borehole, namely:
Ia＝Io+Ic
Wherein Q a is the outlet flow at the wellhead, m 3·s-1;Γa is the annular fluid momentum, kg· (m·s) -1;Ia is the annular fluid total inertia coefficient, kg·m -4;
the observation equation model is expressed as:
Example 4
An extended kalman filter prediction-based deep well overflow condition sensing method is described in embodiment 3, except that in step S3, the state equation model includes: a variation model of pressure difference between a shaft and a stratum, a variation model of annular fluid momentum of the shaft and a variation model of annular fluid mass;
In the variable quantity model of the pressure difference between the well bore and the stratum, the stratum pressure is only related to the depth and does not change along with the drilling time and other parameters, and the change of the stratum pressure along with the depth is random for unpredictable stratum, and the expression is as follows:
In the method, in the process of the invention, Representing the derivative of formation pressure P f with respect to time;
In the well bore annulus fluid momentum change model, according to the conservation of momentum of the fluid in the annulus, and in combination with the well bore-stratum coupling mechanical model, the total momentum change of the annulus drilling fluid is equal to the sum of all forces applied to the fluid at the bottom of the well, and the fluid momentum equation of the well bore annulus is as follows:
In the method, in the process of the invention, Representing the derivative of the annular fluid momentum Γ a with respect to time;
In the annulus fluid mass change model, assuming that the annulus drilling fluid density is constant, the annulus fluid mass change is only related to the volume change of the annulus fluid, and the mass conservation of drilling fluid entering and exiting the mud pit under the normal drilling circulation drilling working condition, namely the volume change of the mud pit is constant; after the kick occurs, stratum fluid invades the shaft, so that the total mass of the fluid in the shaft is increased, the balance of the original drilling fluid in and out is destroyed, and the volume of a mud pit is increased; assuming constant drilling fluid density, the mass change in annulus fluid can be characterized by the fluid reservoir volume change, and the conservation equation is as follows:
In the method, in the process of the invention, The derivative of the volume change V n of the slurry pool with time; q a is the annular outlet flow of the shaft, m 3·s-1;Qp is the inlet flow of the drill pipe, and m 3·s-1; /(I)
To sum up, the state equation model can be expressed as:
Example 5
A deep well overflow condition sensing method based on extended kalman filter prediction as in embodiment 4, except that in step S4, it includes:
s41: linearizing the state equation;
s42: linearizing the observation equation;
s43: discretizing the state equation linearized in the step S41;
S44: and predicting the coupling flow state of the shaft and the stratum in real time by using an extended Kalman filtering prediction method.
Example 6
A deep well overflow condition sensing method based on extended kalman filter prediction as in embodiment 5, except that in steps S41 and S42:
Let state variable x (t) be the change of pressure difference between well bore and stratum, change of annular momentum of well bore and change of annular fluid mass, linearize state equation of state space model of well bore and stratum coupling flow system by Taylor series expansion method, then there are:
f (x) represents a function; delta represents the variation of a certain physical quantity; a 11～a33 is a matrix coefficient after linearization of a state equation;
the observation equation is linearized by the same method, namely, the observation equation of the state space model of the coupling flow system of the well drilling shaft and the stratum is linearized by using the Taylor series expansion method, and the obtained linearization equation is as follows:
Wherein b 11～b33 is a matrix coefficient after linearization of the observation equation.
Preferably, the specific process of step S43 is as follows:
Discretizing the linear state differential matrix by using inverse Laplace variation, namely discretizing the linearized state matrix, wherein the obtained coefficient matrix is marked as A d, and the observation matrix is not a differential equation, so that discretization processing is not needed, and the discretized equation is as follows:
Wherein A d is a state transition matrix, x n is a state change at time n, and x n-1 is a state change at time n-1;
wherein A d＝eAT is a group of the components,
Wherein e is a natural constant, and T is the time interval between data points;
the specific process of step S44 is:
(1) Preliminary prediction of state quantity at time n
xn(-)＝Adxn-1(+)
Wherein x n (-) represents the preliminary predicted state quantity at the time of n, and has no dimension; a d represents a state transition matrix; x n-1 (+) is the corrected predicted state quantity at time n-1, dimensionless, x n-1 (+) is a known quantity, and the initial value is the value obtained in the last step, x n (+)Step (1) corresponds to the discretized state matrix equation of fig. 5;
(2) Preliminary prediction of n-moment covariance transfer matrix
Pn(-)＝AdPn-1(+)Ad T+Qn-1
Wherein P n (-) represents the preliminary covariance transfer matrix at time n; p n-1 (+) represents the corrected covariance transfer matrix at time n-1, P n-1 (+) is a known quantity, and the initial value is the identity matrix using P n (+) obtained in the previous stepQ n-1 represents a state model error matrix at time n-1;
Wherein the method comprises the steps of G= [ 10 ] T, T represents the matrix transpose; t is the time step of Kalman filtering calculation; /(I)Standard deviation of normal distribution of P f;
(3) Calculating the Kalman gain at time n
Wherein H n is the observation coefficient matrix, i.eR n is the positive variance matrix of the system measurement (observation equation) noise,WhereinStandard deviation of normal distribution of P p,Vt,Qa is determined by accuracy of measurement system;
(4) Correcting and predicting state quantity at n time
xn(+)＝xn(-)+Kn[zn-Hnxn(-)]
Wherein x n (+) is a corrected predicted state quantity at the time of n, and has no dimension; z n is the observed variable at time k, which is
(5) Correction prediction of n-moment covariance transfer torque
Pn(+)＝(I-KnHn)Pn(-)(I-KnHn)T+KnRnKn T
Wherein P n (+) is covariance transfer torque at time n, and I is an identity matrix.
Repeating the steps (1) - (5) with x n(+)、Pn (+) as the previous time parameter, wherein x n (+) of each step is the final prediction resultFrom this variation, the formation pressure P f at this time node, the wellbore annulus hydraulic momentum f a, and the predicted mud Chi Zengliang V n can be found.
Firstly, establishing an observation equation model and a state equation model of a state space model of a well drilling shaft and stratum coupling flow system according to the methods in S1, S2 and S3;
then selecting corresponding embodiments according to working conditions:
Drilling conditions: under the condition that the input displacement of a pump is constant, calculating fluid flow friction resistance P rd in a drill pipe of a shaft by using a shaft circulating flow dynamic pressure consumption model, calculating pressure difference P fr of formation pressure and bottom hole pressure by using an inlet and outlet flow difference and formation fluid seepage model, and calculating total inertia coefficient I a of annulus fluid by using a shaft annulus momentum model according to the actual pump displacement; the wellbore annular momentum model is the calculation flow of the definition process of I a above;
Non-drilling conditions: under the condition that the input displacement of a pump is assumed to be zero, calculating fluid flow friction resistance P ra in a well bore annulus by using a well bore circulation flow dynamic pressure consumption model, calculating pressure difference P fr of formation pressure and bottom hole pressure by using an outlet flow and formation fluid seepage model, and calculating an annulus fluid total inertia coefficient I a,Ia＝Io+Ic;
And linearizing an observation equation model and a state equation model of a state space model of a well drilling shaft and stratum coupling flow system according to S41 and S42, and introducing the calculated fluid flow friction resistance P rd in a drill pipe of the well shaft (or fluid flow friction resistance P ra in an annulus of the well shaft), the pressure difference P fr of the stratum pressure and the bottom hole pressure, the total inertia coefficient I a of the annulus fluid and other required known parameters into the linearized state equation and the observation equation.
Discretizing the linearized state equation according to S43 to obtain a discretized state equation.
According to the flow of S44, well selected and processed drilling data (pump pressure P p, inlet and outlet flow difference Q a, slurry pond volume V t), density of drilling fluid required by a wellbore circulation flow dynamic consumption model, rheological parameters of drilling fluid, well depth structure, drilling tool size, fluid rate of formation fluid flowing into a wellbore or into a reservoir required by a formation fluid seepage model, reservoir fluid viscosity, permeability of the reservoir, reservoir depth, skin coefficient, euler-Ma Siqie ronic constant, reservoir porosity, compression coefficient of the reservoir fluid, time of the reservoir section first affected by wellbore pressure, outlet flow required by a wellbore annulus momentum model, all of which should be known amounts) at the current moment are imported, and state quantities (formation pressure (P f), wellbore annulus momentum (r a) and predicted slurry Chi Zengliang (V n)) at the current moment are predicted in a prediction model. Along with the continuous reading of the real-time drilling data, the state quantity is predicted by the prediction model in real time.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (10)
1. The deep well drilling overflow state sensing method based on the extended Kalman filtering prediction is characterized by comprising the following steps of:
s1: establishing a state space model of a well drilling shaft and stratum coupling flow system based on a bonding diagram principle;
S2: establishing an observation equation model of a state space model of a coupling flow system of the drilling shaft and the stratum by utilizing real-time data of logging parameters such as pressure, inlet and outlet flow, slurry pond increment and the like before and after overflow occurs; among pressures before and after overflow occurs, vertical pressure is adopted in drilling circulation working conditions, and casing pressure is adopted in non-drilling circulation working conditions;
s3: establishing a state equation model of a state space model of a well drilling shaft and stratum coupling flow system by using a pore medium seepage theory and an oil and gas well fluid mechanics principle;
s4: and predicting the formation pressure and the coupling flow state of the shaft and the stratum in real time by introducing an extended Kalman filtering prediction method.
2. The extended kalman filter prediction based deep well overflow state sensing method according to claim 1, wherein in step S1, the method for establishing a well bore and stratum coupling flow system state space model based on the bond map principle is as follows:
In a well bore and formation coupled flow system state space model, a pump flow source of known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; the mud tank-like element is modeled as a capacitive element C; the liquid filled conduit is denoted by inertial element I and the fluid friction and thus the pressure drop is denoted by resistive element R; mass conservation is modeled by a common potential junction 0 node, and momentum conservation is modeled by a common current junction 1 node;
the state space model of the coupling flow system of the drilling well shaft and the stratum can be divided into a state space model of the coupling flow system of the drilling well shaft and the stratum during a drilling cycle and a state space model of the coupling flow system of the drilling well shaft and the stratum during a non-drilling cycle according to different working conditions;
the bond map composition of the borehole and formation coupled flow system state space model during the drilling cycle is as follows:
defining a drilling fluid conveying channel from a drilling pump to the bottom of a well, wherein the drilling fluid conveying channel comprises a ground pipeline, a drill string and a drill bit water hole which are 1# co-current junctions 1; defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 2# co-flow junction 1; defining 3# co-current junction 1 from the reservoir to the annulus; defining a well bottom coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward movement as a 1# common potential junction 0;
in a 1# co-flow junction 1 of a drilling fluid conveying channel from a drilling pump to a well bottom, a resistive element comprises a pressure drop coefficient Rrd in a drill rod and a bit partial pressure drop coefficient Rdb, and the pressure drop coefficient Rd and the bit partial pressure drop coefficient Rdb correspond to a drill string circulation pressure loss Prd and a bit partial pressure drop Pdb respectively; the inertia element comprises the inertia Id of drilling fluid in the drill rod, and corresponds to the change rate of the momentum of the drilling fluid in the drill rod The potential source comprises potential source Se of a drilling fluid column in the drill rod, and corresponds to the pressure Pdh of the drilling fluid column in the drill rod; the flow source comprises a pump pressure and displacement flow source Sf of the drilling pump and a flow source Sf flowing out of the drill bit water hole, the pump pressure and displacement flow source Sf of the drilling pump corresponds to the pump pressure Pp and the flow Qp in the drill rod, and the flow source Sf flowing out of the drill bit water hole corresponds to the bottom hole pressure Pbh and the flow Qp in the drill rod;
in the 2# co-current junction 1 of the annulus from the bottom of the annulus to the surface drilling fluid outlet, the potential source comprises potential source Se of the drilling fluid column in the annulus, and corresponds to the annulus fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 3# co-current junction 1 from the reservoir to the annulus, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the potential source comprises a potential source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 1# common potential junction 0, the flow source comprises a flow source Sf flowing out of the water hole of the drill bit, a flow source Sf at the bottom of the annulus and a potential source Sf flowing into the bottom of the well;
because the float valve is arranged in the drill rod, the drill rod is not communicated with the annulus during the pump stopping period, and the bonding diagram of the state space model of the coupling flow system of the drilling shaft and the stratum during the non-drilling circulation period comprises the following components:
Defining an annulus from the bottom of the annulus to a surface drilling fluid outlet as a 4# co-current junction 1; defining a 5# co-current junction 1 from the reservoir to the annulus; defining a bottom hole coalesced by inflow of drill string water hole, invasion of formation fluid and annular upward return as a common potential junction 0;
In the 4# concurrent 1, the potential source comprises potential source Se of an annular drilling fluid column corresponding to annular fluid column pressure Pah; the resistive element comprises an annular pressure drop coefficient Ra and a throttling resistance coefficient Rc, and corresponds to annular circulating pressure consumption Pra and casing pressure Pc respectively; the inertial element comprises the inertia Ia of the fluid in the annular space and corresponds to the change rate of the momentum of the fluid in the annular space The flow source comprises a flow source Sf at the bottom of the annulus, and corresponds to the flow Qa and bottom hole pressure Pbh in the annulus;
In the 5# co-current junction 1, the potential source comprises a formation pressure potential source Se corresponding to formation void pressure Pf; the resistive element comprises a seepage resistance coefficient Rf in the porous medium, and corresponds to the stratum seepage pressure consumption Prf and the flow rate Qf between the shaft and the stratum; the flow source comprises a flow source Sf flowing into the bottom of the well, and corresponds to the flow rate Qf between the well bore and the stratum and bottom hole pressure Pbh;
in the 2# common potential junction 0, the flow source comprises a flow source Sf at the bottom of an annulus and a flow source Sf flowing into the bottom of the well;
and according to the energy flow direction of the bonding diagram material and the law of conservation of the material and the energy, establishing a state space model of a coupling flow system of the drilling well shaft and the stratum.
3. The extended kalman filter prediction based deep well overflow drain state sensing method according to claim 2, wherein in step S2, the observation equation model includes a pressure observation equation model, a volume observation equation model, and a flow observation equation model;
The pressure observation equation model is used for representing various circulation friction conditions generated by the pump pressure in the process of overcoming the fluid flow in the well bore in the drilling circulation drilling process, such as the internal circulation friction of a drill rod, the pressure drop of a drill bit, the circulation friction of the annulus of the well bore and the like; in situ, the drilling pump pressure is equal to the vertical pressure without considering the circulation friction of the surface pipeline, and an equation of the pumping pressure containing the formation pressure is constructed by considering the influence of the formation pressure on the pumping pressure, namely:
Pfr＝Pf-Pbh
p p＝Pf-Pfr+Pdr-Ph during the drilling cycle
P c＝Pf-Pfr-Pra-Pah during non-drilling cycle
Wherein P p is pump pressure, pa; p f is the formation pressure, pa; p fr is the pressure differential of the formation pressure and the bottom hole pressure, pa; p bh is bottom hole pressure, pa; p dr is the fluid flow friction resistance in the wellbore drill pipe, pa; p h is the hydrostatic column pressure in the wellbore drill pipe, pa, P c is the casing pressure, pa; p ra is annular circulating pressure consumption, pa; p ah is the annular liquid column pressure, pa.
4. The extended kalman filter prediction based deep well overflow state sensing method according to claim 3, wherein in step S2, a volume observation equation model is used to characterize the volume data of the mud pit observed by the well drilling monitoring device, and is affected by the errors of the field recorder and the monitoring device, and the observation equation model of the volume of the mud pit is as follows:
Vt＝Vm+Vn
wherein V t is the total pool volume of the slurry pool, m 3;Vm is the standard volume of the slurry pool, m 3;Vn is the volume change amount of the slurry pool, and m 3.
5. The extended kalman filter prediction based deep well overflow state sensing method according to claim 4, wherein in step S2, a flow observation equation model is used for representing the relation of the fluid volume variation in the well bore annulus, and the physical parameters include mass, flow rate, cross-sectional area and the like, and are related to the well bore annulus momentum physical quantity in the state equation, so as to construct an equation of outlet flow and well bore annulus momentum, wherein the definition of the well bore annulus inertia coefficient is the mass variation rate in unit area, and the well bore annulus is divided into two sections to construct the equation, namely an open hole section and a casing section, considering the difference of the well bore annulus cross-sectional areas:
naked eye section:
Casing section:
Wherein Q o is the fluid flow of the open-hole annulus section, m 3·s-1;Qc is the fluid flow of the open-hole annulus section, m 3·s-1;Γo is the fluid momentum of the open-hole annulus section, kg (m.s) -1;Γc is the fluid momentum of the open-hole annulus section, kg (m.s) -1;;Io is the fluid flow inertia coefficient of the open-hole annulus section, kg.m -4;Ic is the fluid flow inertia coefficient of the open-hole annulus section, and kg.m -4; ρ is the annular fluid density, kg.m -3;Ho is the vertical depth of the open hole section of the annulus, m; h c is the vertical depth of the annular sleeve section, m; a o is the cross-sectional area of an open hole section of the annulus, m 2;Ac is the cross-sectional area of a sleeve section of the annulus, m 2;
In actual monitoring of drilling surface equipment, the subsection fluid flow Q o、Qc of the borehole annulus of the open hole section and the casing section cannot be monitored, but the outlet flow at the wellhead is monitored, and the calculation and integration of the subsection fluid flow are integrated by considering that the characterization parameter in the observation equation is one of drilling parameters and the continuity of flow in the borehole, namely:
Wherein Q a is the outlet flow at the wellhead, m 3·s-1;Γa is the annular fluid momentum, kg· (m·s) -1;Ia is the annular fluid total inertia coefficient, kg·m -4;
the observation equation model is expressed as:
6. The extended kalman filter prediction based deep well overflow drain state sensing method according to claim 5, wherein the state equation model in step S3 comprises: a variation model of pressure difference between a shaft and a stratum, a variation model of annular fluid momentum of the shaft and a variation model of annular fluid mass;
In the variable quantity model of the pressure difference between the well bore and the stratum, the stratum pressure is only related to the depth and does not change along with the drilling time and other parameters, and the change of the stratum pressure along with the depth is random for unpredictable stratum, and the expression is as follows:
In the method, in the process of the invention, Representing the derivative of formation pressure P f with respect to time;
In the well bore annulus fluid momentum change model, according to the conservation of momentum of the fluid in the annulus, and in combination with the well bore-stratum coupling mechanical model, the total momentum change of the annulus drilling fluid is equal to the sum of all forces applied to the fluid at the bottom of the well, and the fluid momentum equation of the well bore annulus is as follows:
In the method, in the process of the invention, Representing the derivative of the annular fluid momentum Γ a with respect to time;
In the annulus fluid mass change model, assuming that the annulus drilling fluid density is constant, the annulus fluid mass change is only related to the volume change of the annulus fluid, and the mass conservation of drilling fluid entering and exiting the mud pit under the normal drilling circulation drilling working condition, namely the volume change of the mud pit is constant; after the kick occurs, stratum fluid invades the shaft, so that the total mass of the fluid in the shaft is increased, the balance of the original drilling fluid in and out is destroyed, and the volume of a mud pit is increased; assuming constant drilling fluid density, the mass change in annulus fluid can be characterized by the fluid reservoir volume change, and the conservation equation is as follows:
In the method, in the process of the invention, The derivative of the volume change V n of the slurry pool with time; q a is the annular outlet flow of the shaft, m 3·s-1;Qp is the inlet flow of the drill pipe, and m 3·s-1;
To sum up, the state equation model can be expressed as:
7. the extended kalman filter prediction based deep well overflow drain state sensing method according to claim 6, wherein step S4 comprises:
s41: linearizing the state equation;
s42: linearizing the observation equation;
s43: discretizing the state equation linearized in the step S41;
S44: and predicting the coupling flow state of the shaft and the stratum in real time by using an extended Kalman filtering prediction method.
8. The extended kalman filter prediction based deep well overflow drain state sensing method according to claim 7, wherein in steps S41 and S42:
Let state variable x (t) be the change of pressure difference between well bore and stratum, change of annular momentum of well bore and change of annular fluid mass, linearize state equation of state space model of well bore and stratum coupling flow system by Taylor series expansion method, then there are:
f (x) represents a function; delta represents the variation of a certain physical quantity; a 11～a33 is a matrix coefficient after linearization of a state equation;
the observation equation is linearized by the same method, namely, the observation equation of the state space model of the coupling flow system of the well drilling shaft and the stratum is linearized by using the Taylor series expansion method, and the obtained linearization equation is as follows:
Wherein b 11～b33 is a matrix coefficient after linearization of the observation equation.
9. The extended kalman filter prediction based deep well overflow drain state sensing method according to claim 8, wherein the specific process of step S43 is as follows:
Discretizing the linear state differential matrix by using inverse Laplace variation, namely discretizing the linearized state matrix, and marking the obtained coefficient matrix as A d, wherein the discretized equation is as follows:
Wherein A d is a state transition matrix, x n is a state change at time n, and x n-1 is a state change at time n-1;
Wherein the method comprises the steps of
Where e is a natural constant and T is the time interval between data points.
10. The extended kalman filter prediction based deep well overflow drain state sensing method according to claim 9, wherein the specific process of step S44 is as follows:
(1) Preliminary prediction of state quantity at time n
xn(-)＝Adxn-1(+)
Wherein x n (-) represents the preliminary predicted state quantity at the time of n, and has no dimension; a d represents a state transition matrix; x n-1 (+) is the corrected predicted state quantity at time n-1, dimensionless, x n-1 (+) is a known quantity, and the initial value is the value obtained in the last step, x n (+)
(2) Preliminary prediction of n-moment covariance transfer matrix
Pn(-)＝AdPn-1(+)Ad T+Qn-1
Wherein P n (-) represents the preliminary covariance transfer matrix at time n; p n-1 (+) represents the corrected covariance transfer matrix at time n-1, P n-1 (+) is a known quantity, and the initial value is the identity matrix using P n (+) obtained in the previous stepQ n-1 represents a state model error matrix at time n-1;
Wherein the method comprises the steps of G= [ 10 ] T, T represents the matrix transpose; t is the time step of Kalman filtering calculation; σ Pf is the standard deviation of the normal distribution of P f;
(3) Calculating the Kalman gain at time n
Wherein H n is the observation coefficient matrix, i.eR n is the positive variance matrix of the system measurement noise,WhereinStandard deviation of normal distribution of P p,Vt,Qa is determined by accuracy of measurement system;
(4) Correcting and predicting state quantity at n time
xn(+)＝xn(-)+Kn[zn-Hnxn(-)]
Wherein x n (+) is a corrected predicted state quantity at the time of n, and has no dimension; z n is the observed variable at time k, which is
(5) Correction prediction of n-moment covariance transfer torque
Pn(+)＝(I-KnHn)Pn(-)(I-KnHn)T+KnRnKn T
Wherein P n (+) is covariance transfer torque at time n, and I is an identity matrix;
Repeating the steps (1) - (5) with x n(+)、Pn (+) as the previous time parameter, wherein x n (+) of each step is the final prediction result The formation pressure P f, the well bore annulus hydraulic momentum f a and the predicted mud Chi Zengliang V n at the time node are obtained according to the variation.
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