Deep well overflow state perception method based on extended kalman filter prediction

Abstract

The present application relates to a kind of based on extended Kalman filter prediction deep drilling overflow state perception method, belong to drilling well control technical field, including based on bond graph principle establishes the state space model of drilling wellbore and formation coupling flow system;Real-time data of logging parameters such as pressure before and after overflow occurs, inlet and outlet flow, mud pit increment are used to establish the observation equation model of the state space model of drilling wellbore and formation coupling flow system;The state equation model of the state space model of drilling wellbore and formation coupling flow system is established using pore medium seepage theory and oil and gas well fluid mechanics principle;Formation pressure and wellbore and formation coupling flow state are predicted in real time by introducing extended Kalman filter prediction method.The present application can reduce the false positive rate of system while discovering downhole overflow in advance, effectively reduce the risk of well kick when drilling abnormal high pressure formation, avoid blowout accident, provide safety guarantee for subsequent drilling operation.

Description

TECHNICAL FIELD

[0001] The application relates to a deep well overflow and leakage state sensing method based on extended Kalman filter prediction, and belongs to the technical field of well control. BACKGROUND

[0002] Advanced monitoring and control equipment is often used, for example, conventional pressure control equipment is arranged on low-risk wells, and fine pressure control equipment with advanced downhole measuring instruments is arranged on high-risk or key wells, which well guarantee the safety of drilling in use. However, with the continuous increase of drilling depth, the high-temperature environment of deep strata causes the fine downhole pressure measuring instrument to be unable to be used, which causes the conventional surface pressure control drilling equipment to be relied on on high-risk and key wells. Since the downhole pressure information cannot be obtained, when overflow or well leakage occurs, the on-site personnel cannot discover the downhole overflow and leakage state in time, the well is closed late, the casing pressure is high, and the well control risk is large.

[0003] On the other hand, under the existing conventional pressure control drilling technical framework, an abnormal change in a parameter is usually used to carry out well kick and well leakage monitoring, for example, a person is arranged to observe the mud pit volume. However, when well kick and well leakage occur, the actual situation is that multiple parameters change abnormally at the same time, and the changes are internally related and have the characteristics of multiple parameter cooperative response, so a system modeling method needs to be used to realize the monitoring of the overflow and leakage state. It is urgent to use the multi-source information fusion technical means under the guidance of the new theoretical method to realize the timely prediction of the downhole overflow and leakage information based on the surface logging data under the existing conventional pressure control drilling technical framework, and to avoid a series of well control risks caused by overflow and leakage monitoring delay. SUMMARY

[0004] In order to solve the problems of the prior art, the application discloses a downhole overflow and leakage state early identification method for deep well and ultra-deep well drilling by using conventional pressure control drilling technology, which can discover the downhole overflow and leakage in advance and reduce the system false alarm rate, effectively reduce the well kick risk of drilling through an abnormal high-pressure stratum, avoid well blowout accidents, and provide safety protection for subsequent drilling operations.

[0005] The application adopts the following technical scheme:

[0006] A deep well overflow and leakage state sensing method based on extended Kalman filter prediction comprises the following steps:

[0007] S1: a state space model of a drilling wellbore and stratum coupling flow system is established based on the principle of bond graph;

[0008] S2: using the real-time data of the overflow pressure before and after (the stand pressure is used in the drilling circulation condition, and the casing pressure is used in the non-drilling circulation condition), the inlet and outlet flow, and the mud pit increment to establish the observation equation model of the state space model of the drilling wellbore and formation coupling flow system;

[0009] S3: using the permedial seepage theory and the oil and gas well fluid mechanics principle to establish the state equation model of the state space model of the drilling wellbore and formation coupling flow system;

[0010] S4: introducing the extended Kalman filter prediction method to predict the formation pressure (pore and leakage) and the real-time state of the wellbore and formation coupling flow in real time.

[0011] Preferably, in step S1, the method for establishing the state space model of the drilling wellbore and formation coupling flow system based on the bond graph principle is as follows:

[0012] In the state space model of the drilling wellbore and formation coupling flow system, the pump flow source with known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; the elements similar to the mud tank (such as the mud pit) are modeled as capacitive elements C; the pipelines filled with liquid are represented by inertial elements I, and the fluid friction and the pressure drop generated thereby are represented by resistive elements R; the mass conservation is modeled by the common potential junction 0 node, and the momentum conservation is modeled by the common flow junction 1 node;

[0013] The state space model of the drilling wellbore and formation coupling flow system can be divided into the state space model of the drilling wellbore and formation coupling flow system during the drilling circulation and the state space model of the drilling wellbore and formation coupling flow system during the non-drilling circulation according to different working conditions.

[0014] The bond graph of the state space model of the drilling wellbore and formation coupling flow system during the drilling circulation is composed of the following:

[0015] The drilling fluid conveying channel from the drilling pump to the bottom hole is defined as the 1# common flow junction 1 (left), including the surface pipeline, the drill string, and the drill bit water hole; the annulus from the bottom hole to the ground drilling fluid outlet is defined as the 2# common flow junction 1 (right); the reservoir to the annulus is defined as the 3# common flow junction 1 (down); and the bottom hole gathered by the drill string water hole, the formation fluid invasion, and the annulus upflow is defined as the 1# common potential junction 0.

[0016] In the 1# common flow junction 1 of the drilling fluid conveying channel from the drilling pump to the bottom hole, the resistive elements include the drill pipe internal pressure drop coefficient Rrd and the drill bit local pressure drop coefficient Rdb, which correspond to the drill string circulation pressure consumption Prd and the drill bit local pressure drop Pdb, respectively; the inertial element includes the drill pipe internal drilling fluid inertia Id, which corresponds to the drill pipe internal drilling fluid momentum change rate d; the potential source includes a potential source Se of the drilling fluid column in the drill pipe, corresponding to the drilling fluid column pressure Pdh in the drill pipe; the flow source includes a flow source Sf of the pump pressure and displacement of the drilling pump and a flow source Sf flowing out of the drill bit water hole, the flow source Sf of the pump pressure and displacement of the drilling pump corresponding to the pump pressure Pp and the flow rate Qp in the drill pipe, and the flow source Sf flowing out of the drill bit water hole corresponding to the bottom hole pressure Pbh and the flow rate Qp in the drill pipe;

[0017] In the 2# co-flow junction 1 from the annulus bottom hole to the annulus of the drilling fluid outlet on the ground, the potential source includes a potential source Se of the drilling fluid column in the annulus, corresponding to the annulus column pressure Pah; the resistive element includes an annulus pressure drop coefficient Ra and a throttle resistance coefficient Rc, corresponding to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the fluid inertia Ia in the annulus, corresponding to the fluid momentum change rate a; the flow source includes a flow source Sf at the bottom of the annulus, corresponding to the flow rate Qa in the annulus and the bottom hole pressure Pbh;

[0018] In the 3# co-flow junction 1 from the reservoir to the annulus, the potential source includes a formation pressure potential source Se, corresponding to the formation pore pressure Pf; the resistive element includes a porous medium seepage resistance coefficient Rf, corresponding to the formation seepage pressure loss Prf and the flow rate Qf between the wellbore and the formation; the potential source includes a potential source Sf flowing into the bottom hole, corresponding to the flow rate Qf between the wellbore and the formation and the bottom hole pressure Pbh;

[0019] In the 1# co-potential junction 0, the flow source includes a flow source Sf flowing out of the drill bit water hole, a flow source Sf at the bottom of the annulus, and a potential source Sf flowing into the bottom hole;

[0020] Because the float valve is installed in the drill pipe, the drill pipe is not connected with the annulus during pump stopping, and the bond graph of the state space model of the coupling flow system of the drilling wellbore and the formation during non-drilling circulation is as follows:

[0021] The annulus from the annulus bottom hole to the drilling fluid outlet on the ground is defined as the 4# co-flow junction 1; the reservoir to the annulus is defined as the 5# co-flow junction 1; and the bottom hole gathered by the flow into the drill string water hole, the formation fluid invasion and the annulus upward return is defined as the co-potential junction 0;

[0022] In the 4# co-flow junction 1, the potential source includes a potential source Se of the drilling fluid column in the annulus, corresponding to the annulus column pressure Pah; the resistive element includes an annulus pressure drop coefficient Ra and a throttle resistance coefficient Rc, corresponding to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the fluid inertia Ia in the annulus, corresponding to the fluid momentum change rate a; the flow source includes a flow source Sf at the bottom of the annulus, corresponding to the flow rate Qa in the annulus and the bottom hole pressure Pbh;

[0023] 5# in the co-flow junction, the potential source includes formation pressure potential source Se, corresponding to the formation pore pressure Pf; resistive elements include the seepage resistance coefficient Rf in the porous medium, corresponding to the formation seepage pressure consumption Prf and the wellbore and formation flow Qf; the flow source includes the flow source Sf flowing into the well bottom, corresponding to the wellbore and formation flow Qf and the well bottom pressure Pbh;

[0024] 2# in the co-potential junction 0, the flow source includes the flow source Sf at the bottom of the annulus and the flow source Sf flowing into the well bottom;

[0025] According to the bonding graph material energy flow direction, combined with the conservation of mass and energy, the state space model of the coupling flow system of the wellbore and the formation is established.

[0026] 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;

[0027] The pressure observation equation model is used to characterize the pump pressure in the process of drilling circulation drilling to overcome various circulating friction generated by the fluid flow in the wellbore, such as circulating friction in the drill pipe, drill bit pressure drop, wellbore annulus circulating friction, etc.; the pump pressure is equivalent to the standpipe pressure in the field without considering the ground pipeline circulating friction, considering the influence of formation pressure on pump pressure, the equation of pump pressure containing formation pressure is constructed, that is:

[0028]

[0029] , during drilling circulation

[0030] , during non-drilling circulation

[0031] In the formula, P p Pump pressure, Pa; P f Formation pressure, Pa; P fr Pressure difference between formation pressure and well bottom pressure, Pa; P bh Well bottom pressure, Pa; P dr Friction resistance of fluid flow in wellbore drill pipe, Pa; h Static fluid column pressure of fluid flow in wellbore drill pipe, Pa, Casing pressure, Pa; Annulus circulating pressure consumption, Pa; Annulus fluid column pressure, Pa.

[0032] Preferably, in step S2, the volume observation equation model is used to represent the mud pit volume data observed by the drilling monitoring equipment, which is affected by the errors of the field recorders and the monitoring equipment. The observation equation model of the mud pit volume is as follows:

[0033]

[0034] wherein, V t Vpit is the total pit volume of the mud pit, m 3 ; V m Vnorm is the standard volume of the mud pit, m 3 ; V n ΔVpit is the volume change of the mud pit, m 3 .

[0035] Preferably, in step S2, the flow observation equation model is used to represent the relationship between the fluid volume change in the wellbore annulus and the physical parameters such as mass, flow rate and cross-sectional area, which is related to the momentum physical quantity in the state equation. Therefore, the equations of the outlet flow and the wellbore annulus momentum are constructed, wherein the definition of the wellbore annulus inertia coefficient is the mass change rate per unit area. Considering the different cross-sectional areas of the drilling wellbore annulus, the drilling wellbore annulus is divided into two sections to establish the equations, which are the open hole section and the casing section (the upper part of the actual wellbore with casing is the casing section, and the lower part without casing is the open hole section):

[0036] Open hole section:

[0037] Casing section:

[0038] wherein, Q o Qopen is the fluid flow of the open hole section of the annulus, m 3 ·s -1 ; Q c Qcasing is the fluid flow of the casing section of the annulus, m 3 ·s -1 ; I o Mopen is the fluid momentum of the open hole section of the annulus, kg·(m·s) -1 ; I c Mcasing is the fluid momentum of the casing section of the annulus, kg·(m·s) -1 ; I o Copen is the fluid flow inertia coefficient of the open hole section of the annulus, kg·m -4 ; I cThe fluid inertia coefficient for the annular casing section is given in kg·m. -4 ; p The density of the annular fluid is kg·m³. -3 ; H o The vertical depth of the annular naked-eye segment is in meters (m). H c The vertical depth of the annular casing section is in meters (m). A o Let m be the cross-sectional area of ​​the annular naked eye segment. 2 ; A c The cross-sectional area of ​​the annular casing section is m. 2 ;

[0039] In actual drilling surface equipment monitoring, the segmented fluid flow rates in the open hole section and casing section of the wellbore annulus are monitored. Q o , Since monitoring is not possible, only the outlet flow rate at the wellhead is monitored. Considering that the characteristic parameter in the observation equation is one of the drilling parameters and the flow within the wellbore is continuous, the above segmented flow rate calculations are integrated, i.e.:

[0040] ,

[0041] In the formula, Q a The outlet flow rate at the wellhead is m. 3 ·s -1 ; I a Let be the momentum of the annular fluid, kg·(m·s). -1 ; I a The total inertia coefficient of the annular fluid is expressed in kg·m. -4 ;

[0042] The observation equation model is expressed as:

[0043] During drilling cycle

[0044] During non-drilling cycles.

[0045] Preferably, the state equation model in step S3 includes: a model of the change in pressure difference between the wellbore and the formation, a model of the change in momentum of the annular fluid in the wellbore, and a model of the change in mass of the annular fluid.

[0046] In the model of the change in pressure difference between the wellbore and the formation, the formation pressure is only related to the depth and does not change with drilling time or other parameters. Furthermore, for unpredictable formations, the change in formation pressure with depth is random. Its expression is as follows:

[0047]

[0048] wherein, represents the formation pressure P f derivative with respect to time;

[0049] In the wellbore annulus fluid momentum change model, according to the momentum conservation relationship of the fluid in the annulus, combined with the wellbore-formation coupling mechanics model, the total momentum change of the annulus drilling fluid is equal to the total force applied on the fluid at the bottom, The fluid momentum equation of the wellbore annulus is as follows:

[0050]

[0051] wherein, represents the annulus fluid momentum I a derivative with respect to time;

[0052] In the annulus fluid mass change model, it is assumed that the annulus drilling fluid density is constant, and the mass change of the annulus fluid is only related to the volume change of the annulus fluid. Under normal drilling circulating drilling conditions, the mass conservation of drilling fluid entering and leaving the mud pit is constant, that is, the volume change of the mud pit is constant. After the well kick occurs, the formation fluid invades the wellbore, resulting in an increase in the total mass of the fluid in the wellbore, which destroys the original balance of drilling fluid entering and leaving, and thus causes the volume of the mud pit to increase. Assuming that the drilling fluid density is constant, the mass change of the annulus fluid can be represented by the volume change of the drilling fluid pit, and the conservation equation is as follows:

[0053]

[0054] wherein, is the volume change of the mud pit V n derivative with respect to time; Q a is the wellbore annulus outlet flow rate, m 3 ·s -1 ; Q p is the drill pipe inlet flow rate, m 3 ·s -1 ;

[0055] Therefore, the state equation model can be represented as:

[0056] .

[0057] Preferably, step S4 comprises:

[0058] S41: linearizing the state equation;

[0059] S42: linearizing the observation equation;

[0060] S43: discretizing the state equation linearized in step S41;

[0061] S44: predicting the coupling flow state of the wellbore and the formation in real time by using the extended Kalman filter prediction method.

[0062] Preferably, in steps S41 and S42:

[0063] Let the state variable x ( t ) be the change in the pressure difference between the wellbore and the formation, the change in the annular momentum of the wellbore, and the change in the mass of the annular fluid, and linearize the state equation of the state space model of the coupling flow system of the drilling wellbore and the formation by using the Taylor series expansion method, so that:

[0064]

[0065] denotes a function; denotes the change in a physical quantity; ~ is the matrix coefficient after linearization of the state equation;

[0066] The observation equation is linearized in the same way, i.e., linearize the observation equation of the state space model of the coupling flow system of the drilling wellbore and the formation by using the Taylor series expansion method, and the linearized equation is as follows:

[0067]

[0068] In the formula, ~ is the matrix coefficient after linearization of the observation equation.

[0069] Preferably, the specific process of step S43 is as follows:

[0070] Discretize the linear state differential matrix by using the inverse Laplace transform, i.e., discretize the linearized state matrix, and the coefficient matrix obtained is denoted as A d , and the observation matrix is not a differential equation, so it does not need to be discretized, and the discretized equation is as follows:

[0071]

[0072] In the formula, A d is the state transition matrix, x n is the state change at time n, x n-1 is the state change at time n-1.

[0073] wherein ,

[0074] wherein e is a natural constant and T is the time interval between data points;

[0075] Preferably, the specific process of step S44 is as follows:

[0076] (1) Preliminary prediction n State quantity at time

[0077]

[0078] wherein x n (-) represents the preliminary predicted state quantity at time n , dimensionless; represents the state transition matrix; x n-1 (+) is the modified predicted state quantity at time n -1, dimensionless, x n-1 (+) is a known quantity, using the obtained x n (+) of the previous step, the initial value is ; step (1) corresponds to the discretized state matrix equation of Figure 5 ;

[0079] (2) Preliminary prediction of the covariance transition matrix at time n

[0080]

[0081] wherein represents the preliminary covariance transition matrix at time n ; represents the modified covariance transition matrix at time n -1, is a known quantity, using the obtained , the initial value is the unit matrix ; represents the state model error matrix at time n-1;

[0082] wherein ; , T represents the matrix transpose; T is the time step of the Kalman filter calculation; is the standard deviation of the normal distribution of f ;

[0083] (3) Calculate the Kalman gain at time n ​

[0084]

[0085] in, H n The observation coefficient matrix, i.e. ; R n It is the positive definite variance matrix of the system measurement (observation equation) noise. ,in , , P respectively p V t Q a The standard deviation of the normal distribution is determined by the accuracy of the measurement system;

[0086] (4) Correct the predicted state variables at time n

[0087]

[0088] in, x n (+) is n The time-varying predicted state quantity is dimensionless; for k The observed variable at time t is ;

[0089] (5) Revised forecast n Moment covariance transfer torque

[0090]

[0091] in, for n Covariance transfer torque at time t, I It is an identity matrix.

[0092] Will , Using the parameters from the previous time step, repeat steps (1) to (5), each step... For the final prediction result The formation pressure at that time point can be calculated based on this change. P f Hydraulic momentum of the wellbore annulus G a and the predicted increase in mud pits V n .

[0093] For any details not covered in this invention, please refer to the prior art.

[0094] The beneficial effects of this invention are as follows:

[0095] The present application can greatly shorten the identification time after overflow or well leakage occurs, provide sufficient reaction time for timely well shut-in on site, effectively reduce the risk of high casing pressure formed during well shut-in and well killing, avoid the risk of well kick and blowout caused by late discovery of overflow, and provide more accurate formation pressure information for subsequent drilling operations, technical support for ensuring the safety of on-site operations, protection of on-site personnel safety, and avoidance of property loss.

[0096] The present application can reduce the amount of formation fluid invasion when overflow is discovered, and reduce the difficulty of subsequent well killing. BRIEF DESCRIPTION OF DRAWINGS

[0097] The drawings accompanying the specification of this application are used to provide a further understanding of the present application, the illustrative embodiments of the present application and their descriptions serve to explain the present application, and do not constitute an improper limitation on the present application.

[0098] Figure 1 Flowchart for an embodiment of the present application;

[0099] Figure 2 Physical model of the coupling flow state space of the wellbore and the formation during drilling circulation and pump stoppage;

[0100] Figure 3 Bond graph of the established coupling flow state space model of the wellbore and the formation during drilling;

[0101] Figure 4 Bond graph of the established coupling flow state space model of the wellbore and the formation during non-drilling circulation;

[0102] Figure 5 Flowchart of the overflow state extended Kalman filter prediction of the wellbore-formation coupling flow system. DETAILED DESCRIPTION

[0103] In order to better understand the technical solutions in the specification by those skilled in the art, the technical solutions in the embodiments of the specification will be described clearly and completely below with reference to the drawings in the specification, but are not limited thereto, and the present application is not described in detail.

[0104] Embodiment 1

[0105] A deep drilling overflow state sensing method based on extended Kalman filter prediction, like Figure 1 , includes the following steps:

[0106] S1: Establish a state space model of a drilling wellbore and formation coupling flow system based on the principle of bond graph;

[0107] S2: Establishing an observation equation model of the state space model of the coupled flow system of the wellbore and the formation by using real-time data of mud logging parameters such as the pressure before and after overflow, the inlet and outlet flow, and the mud pit increment;

[0108] S3: Establishing a state equation model of the state space model of the coupled flow system of the wellbore and the formation by using the permedial seepage theory and the oil and gas well fluid mechanics principle;

[0109] S4: Real-time predicting the formation pressure and the coupled flow state of the wellbore and the formation by introducing the extended Kalman filter prediction method.

[0110] Embodiment 2

[0111] A deep drilling overflow state sensing method based on the extended Kalman filter prediction, as described in Embodiment 1, except that, as shown in Figures 2-4 In step S1, the method for establishing the state space model of the coupled flow system of the wellbore and the formation based on the bond graph principle is as follows:

[0112] In the state space model of the coupled flow system of the wellbore and the formation, the pump flow source with known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; elements similar to mud tanks (such as mud pits) are modeled as capacitive elements C; pipelines filled with liquid are represented by inertial elements I, and fluid friction and the pressure drop generated thereby are represented by resistive elements R; mass conservation is modeled by a common potential junction 0 node, and momentum conservation is modeled by a common flow junction 1 node;

[0113] The state space model of the coupled flow system of the wellbore and the formation can be divided into a state space model of the coupled flow system of the wellbore and the formation during drilling circulation and a state space model of the coupled flow system of the wellbore and the formation during non-drilling circulation according to different working conditions;

[0114] The bond graph of the state space model of the coupled flow system of the wellbore and the formation during drilling circulation is composed of:

[0115] The drilling fluid conveying channel from the drilling pump to the bottom hole is defined as the 1# common flow junction 1 (left), including the surface pipeline, the drill string, and the drill bit water hole; the annulus from the bottom hole to the ground drilling fluid outlet is defined as the 2# common flow junction 1 (right); the reservoir to the annulus is defined as the 3# common flow junction 1 (down); and the bottom hole gathered by the drill string water hole inflow, the formation fluid invasion, and the annulus upflow is defined as the 1# common potential junction 0;

[0116] In the 1# co-flow junction of the drilling fluid delivery channel from the drilling pump to the bottom hole, the resistive element includes the drilling pipe internal pressure drop coefficient Rrd and the drill bit local pressure drop coefficient Rdb, which correspond to the drilling string circulating pressure loss Prd and the drill bit local pressure drop Pdb respectively; the inertial element includes the drilling fluid inertia Id in the drilling pipe, which corresponds to the drilling fluid momentum change rate in the drilling pipe d; the potential source includes the potential source Se of the drilling fluid liquid column in the drilling pipe, which corresponds to the drilling fluid liquid column pressure Pdh; the flow source includes the flow source Sf of the pump pressure and displacement of the drilling pump and the flow source Sf out of the drill bit water hole, the flow source Sf of the pump pressure and displacement of the drilling pump corresponding to the pump pressure Pp and the flow rate Qp in the drilling pipe, and the flow source Sf out of the drill bit water hole corresponding to the bottom hole pressure Pbh and the flow rate Qp in the drilling pipe;

[0117] In the 2# co-flow junction of the annulus from the bottom hole to the ground drilling fluid outlet, the potential source includes the potential source Se of the annulus drilling fluid liquid column, which corresponds to the annulus liquid column pressure Pah; the resistive element includes the annulus internal pressure drop coefficient Ra and the choke resistance coefficient Rc, which correspond to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the annulus internal fluid inertia Ia, which corresponds to the annulus internal fluid momentum change rate a; the flow source includes the flow source Sf at the bottom of the annulus, which corresponds to the flow rate Qa in the annulus and the bottom hole pressure Pbh;

[0118] In the 3# co-flow junction from the reservoir to the annulus, the potential source includes the formation pressure potential source Se, which corresponds to the formation pore pressure Pf; the resistive element includes the porous medium internal seepage resistance coefficient Rf, which corresponds to the formation seepage pressure loss Prf and the flow rate Qf between the wellbore and the formation; the potential source includes the potential source Sf flowing into the bottom hole, which corresponds to the flow rate Qf between the wellbore and the formation and the bottom hole pressure Pbh;

[0119] In the 1# co-potential junction 0, the flow source includes the flow source Sf out of the drill bit water hole, the flow source Sf at the bottom of the annulus and the potential source Sf flowing into the bottom hole;

[0120] Because the float valve is installed in the drilling pipe, the drilling pipe is not connected with the annulus during pump stopping, and the bond graph of the state space model of the coupling flow system of the drilling wellbore and the formation during non-drilling circulation is composed as follows:

[0121] The annulus from the bottom hole of the annulus to the ground drilling fluid outlet is defined as the 4# co-flow junction 1; the annulus from the reservoir to the annulus is defined as the 5# co-flow junction 1; the bottom hole gathered by the flow into the drill string water hole, the formation fluid invasion and the annulus upward return is defined as the co-potential junction 0;

[0122] In the 4# co-flow junction 1, the potential source includes the potential source Se of the annulus drilling fluid liquid column, which corresponds to the annulus liquid column pressure Pah; the resistive element includes the annulus internal pressure drop coefficient Ra and the choke resistance coefficient Rc, which correspond to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the annulus internal fluid inertia Ia, which corresponds to the annulus internal fluid momentum change rate a; flow source Sf, corresponding to annulus flow rate Qa and bottom hole pressure Pbh;

[0123] 5# in the co-flow junction, potential source Se, corresponding to formation pore pressure Pf; resistive element Rf, corresponding to formation seepage pressure loss Prf and wellbore-formation flow rate Qf; flow source Sf, corresponding to wellbore-formation flow rate Qf and bottom hole pressure Pbh;

[0124] 2# in the co-potential junction 0, flow source Sf and Sf;

[0125] According to the bonding graph material energy flow direction, combined with the law of conservation of mass and energy, the state space model of the coupling flow system of the wellbore and the formation is established.

[0126] Example 3

[0127] A deep drilling overflow state sensing method based on extended Kalman filter prediction, as described in example 2, except 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;

[0128] The pressure observation equation model is used to characterize the situation that the pump pressure overcomes various circulating friction losses generated by the fluid flow in the wellbore during the drilling circulation drilling, such as the circulating friction loss in the drill pipe, the drill bit pressure drop, the wellbore annulus circulating friction loss, etc. In the field, the drilling pump pressure is equivalent to the standpipe pressure without considering the ground pipeline circulating friction loss. Considering the influence of the formation pressure on the pump pressure, the equation of the pump pressure containing the formation pressure is constructed, that is:

[0129]

[0130] , during drilling circulation

[0131] , during non-drilling circulation

[0132] In the formula, P p Pa is the pump pressure, Pa; P f Pf is the formation pressure, Pa; P fr is the pressure difference between the formation pressure and the bottom hole pressure, Pa; P bh Pbh is the bottom hole pressure, Pa; P dr is the friction resistance of the fluid flow in the wellbore drill pipe, Pa; P h is the hydrostatic pressure of the fluid in the wellbore drill pipe, Pa, Pa; Pa; Pa;

[0133] Preferably, in step S2, the volume observation equation model is used to represent the mud pit volume data observed by the drilling monitoring equipment. The observation equation model of the mud pit volume is as follows, which is affected by the errors of the field recorders and the monitoring equipment:

[0134]

[0135] In the formula, V t Pa; 3 ; V m Pa; 3 ; V n Pa; 3 .

[0136] Preferably, in step S2, the flow observation equation model is used to represent the relationship between the fluid volume change in the wellbore annulus and the physical parameters such as mass, flow rate and cross-sectional area, which is related to the momentum physical quantity in the state equation. Therefore, the equations of outlet flow and wellbore annulus momentum are constructed, and the definition of the wellbore annulus inertia coefficient is the mass change rate per unit area. Considering the different cross-sectional areas of the drilling wellbore annulus, the drilling wellbore annulus is divided into two sections to establish the equations, which are the open hole section and the casing section (the upper part of the actual wellbore with casing is the casing section, and the lower part without casing is the open hole section):

[0137] Open hole section:

[0138] Casing section:

[0139] In the formula, Q o Pa; 3 ·s -1 ; Q c Pa; 3 ·s -1 ; I o kg·(m·s) -1 ; I c kg·(m·s) -1 ;; Io The fluid inertia coefficient in the annular naked-eye section is expressed in kg·m. -4 ; I c The fluid inertia coefficient for the annular casing section is given in kg·m. -4 ; p The density of the annular fluid is kg·m³. -3 ; H o The vertical depth of the annular naked-eye segment is in meters (m). H c The vertical depth of the annular casing section is in meters (m). A o Let m be the cross-sectional area of ​​the annular naked eye segment. 2 ; A c The cross-sectional area of ​​the annular casing section is m. 2 ;

[0140] In actual drilling surface equipment monitoring, the segmented fluid flow rates in the open hole section and casing section of the wellbore annulus are monitored. Q o , Since monitoring is not possible, only the outlet flow rate at the wellhead is monitored. Considering that the characteristic parameter in the observation equation is one of the drilling parameters and the flow within the wellbore is continuous, the above segmented flow rate calculations are integrated, i.e.:

[0141] ,

[0142] In the formula, Q a The outlet flow rate at the wellhead is m. 3 ·s -1 ; I a Let be the momentum of the annular fluid, kg·(m·s). -1 ; I a The total inertia coefficient of the annular fluid is expressed in kg·m. -4 ;

[0143] The observation equation model is expressed as:

[0144] During drilling cycle

[0145] During non-drilling cycles.

[0146] Example 4

[0147] A deep well overflow state sensing method based on extended Kalman filter prediction, as described in Embodiment 3, except that in step S3, the state equation model comprises: a wellbore and formation pressure differential change amount model, a wellbore annulus fluid momentum change amount model, and an annulus fluid mass change amount model;

[0148] In the wellbore and formation pressure differential change amount model, the formation pressure is only related to the depth and does not change with the drilling time and other parameters, and for unpredictable formations, the change of the formation pressure with the depth has randomness, and its expression is as follows:

[0149]

[0150] In the formula, Pf represents the formation pressure P f derivative with respect to time;

[0151] In the wellbore annulus fluid momentum change amount model, according to the momentum conservation relationship of the fluid in the annulus, combined with the wellbore-formation coupling mechanics model, the total momentum change amount of the annulus drilling fluid is equal to the total sum of all forces applied to the fluid at the bottom, The fluid momentum equation of the wellbore annulus is as follows:

[0152]

[0153] In the formula, Pf represents the annulus fluid momentum I a derivative with respect to time;

[0154] In the annulus fluid mass change amount model, it is assumed that the annulus drilling fluid density is constant, and the mass change amount of the annulus fluid is only related to the volume change of the annulus fluid. Under normal drilling circulation drilling conditions, the mass of the drilling fluid entering and leaving the mud pit is conserved, that is, the volume change amount of the mud pit is constant. After the well kick occurs, the formation fluid invades the wellbore, causing the total mass of the fluid in the wellbore to increase, which destroys the original balance of the drilling fluid entering and leaving, and thus causes the volume of the mud pit to increase. Assuming that the drilling fluid density is constant, the mass change amount of the annulus fluid can be represented by the volume change amount of the drilling fluid pit, and its conservation equation is as follows:

[0155]

[0156] In the formula, V represents the volume change amount of the mud pit V n derivative with respect to time; Q a Qout represents the wellbore annulus outlet flow rate, m 3 ·s -1 ; Q p Qin represents the drill pipe inlet flow rate, m3 ·s -1 ;

[0157] In summary, the state equation model can be expressed as:

[0158] .

[0159] Example 5

[0160] A deep well overflow and leakage state perception method based on extended Kalman filter prediction, as described in Example 4, except that step S4 includes:

[0161] S41: linearizing the state equation;

[0162] S42: linearizing the observation equation;

[0163] S43: discretizing the state equation linearized in step S41;

[0164] S44: using the extended Kalman filter prediction method to perform real-time prediction on the wellbore and formation coupling flow state.

[0165] Example 6

[0166] A deep well overflow and leakage state perception method based on extended Kalman filter prediction, as described in Example 5, except that steps S41 and S42 include:

[0167] Let the state variable x ( t ) be the change in wellbore and formation pressure difference, wellbore annulus momentum change, and annulus fluid mass change, and linearize the state equation of the state space model of the drilling wellbore and formation coupling flow system using the Taylor series expansion method, then:

[0168]

[0169] denotes a certain function; denotes the change in a certain physical quantity; ~ is the matrix coefficient after linearization of the state equation;

[0170] The observation equation is linearized in the same way, i.e., linearize the observation equation of the state space model of the drilling wellbore and formation coupling flow system using the Taylor series expansion method, and the linearized equation is as follows:

[0171]

[0172] In the formula, ~ These are the matrix coefficients after linearizing the observation equation.

[0173] Preferably, the specific process of step S43 is as follows:

[0174] Discretizing the linear state differential matrix using the inverse Laplace transform, i.e., discretizing the linearized state matrix, yields a coefficient matrix denoted as A. d Since the observation matrix is ​​not a differential equation, it does not require discretization. The discretized equation is as follows:

[0175]

[0176] In the formula, A d Here is the state transition matrix. x n For the state change at time n, x n-1 This represents the state change at time n-1;

[0177] in ,

[0178] In the formula, e is the natural constant, and T is the time interval between data points;

[0179] The specific process of step S44 is as follows:

[0180] (1) Preliminary forecast n Time-state quantity

[0181]

[0182] in, x n (-)express n The initial predicted state quantity at time t is dimensionless; Represents the state transition matrix; x n-1 (+) is n The corrected predicted state quantity at time -1 is dimensionless. x n-1 (+) represents a known quantity, obtained from the previous step. x n (+), initial value is Step (1) corresponds to Figure 5 Discretized state matrix equations;

[0183] (2) Preliminary prediction of the covariance transition matrix at time n

[0184]

[0185] in, express nThe initial covariance transition matrix at time t; express n The corrected covariance transition matrix at time -1 Given the quantities, use the values ​​obtained in the previous step. The initial value is the identity matrix. ; This represents the error matrix of the state model at time n-1;

[0186] in ; T represents the matrix transpose; T The time step is calculated for the Kalman filter; For P f The standard deviation of the normal distribution;

[0187] (3) Calculation n Time-based Kalman gain

[0188]

[0189] in, H n The observation coefficient matrix, i.e. ; R n It is the positive definite variance matrix of the system measurement (observation equation) noise. ,in , , P respectively p V t Q a The standard deviation of the normal distribution is determined by the accuracy of the measurement system;

[0190] (4) Correct the predicted state variables at time n

[0191]

[0192] in, x n (+) is n The time-varying predicted state quantity is dimensionless; for k The observed variable at time t is ;

[0193] (5) Revised forecast n Moment covariance transfer torque

[0194]

[0195] in, for n Covariance transfer torque at time t,I It is an identity matrix.

[0196] Will , Using the parameters from the previous time step, repeat steps (1) to (5), each step... For the final prediction result The formation pressure at that time point can be calculated based on this change. P f Hydraulic momentum of the wellbore annulus G a and the predicted increase in mud pits V n .

[0197] In this invention, firstly, the observation equation model and the state equation model of the state space model of the coupled flow system between the wellbore and the formation are established according to the methods in S1, S2 and S3;

[0198] Then, select the appropriate implementation plan based on the working conditions:

[0199] Drilling conditions: Assuming a constant pump input displacement, the frictional resistance of the fluid flow inside the drill pipe is calculated using a wellbore circulation pressure loss model based on the actual pump displacement. P rd The pressure difference between formation pressure and bottom hole pressure is calculated using the inlet / outlet flow difference and formation fluid seepage model. P fr Calculate the total inertia coefficient of the annulus fluid using the wellbore annulus momentum model. I a Among them, the wellbore circulating flow pressure loss model and the formation fluid seepage model are conventional formulas used in drilling, while the wellbore annulus momentum model is the one mentioned above. I a The calculation process of the definition process;

[0200] Non-drilling conditions: Under the assumption that the pump's input displacement is zero, the frictional resistance of the fluid flow in the wellbore annulus is calculated using a wellbore circulation flow pressure loss model. P ra The pressure difference between formation pressure and bottom hole pressure is calculated using the outlet flow rate and formation fluid seepage model. P fr Calculate the total inertia coefficient of the annular fluid. I a , ;

[0201] The observation equation model and state equation model of the coupled flow system between the wellbore and the formation are linearized according to S41 and S42, and the calculated fluid flow friction resistance inside the wellbore and drill pipe is then applied. P rd(or fluid flow friction resistance in the wellbore annulus P ra , the differential pressure between the formation pressure and the bottom hole pressure P fr , the total annulus fluid inertia coefficient I a and other required known parameters into the linearized state equation and the observation equation.

[0202] discretize the linearized state equation according to S43 to obtain a discretized state equation.

[0203] According to the flow of S44, the selected and processed drilling data at the current time (pump pressure P p , the inlet and outlet flow difference Q a , the mud pit volume V t , the drilling fluid density, the drilling fluid rheological parameters, the well depth structure, the drilling tool size required by the wellbore circulation flow pressure consumption model, the reservoir fluid inflow rate into the wellbore or the wellbore inflow rate into the reservoir, the reservoir fluid viscosity, the reservoir permeability, the reservoir depth, the skin factor, the Euler-Mascheroni constant, the reservoir porosity, the reservoir fluid compressibility, the time when the reservoir section is first affected by the wellbore pressure, the outlet flow required by the wellbore annulus momentum model, all of which should be known quantities), the state quantity at the current time (the formation pressure (Pf) P f ), the wellbore annulus hydraulic momentum (M G a ) and the predicted mud pit increment (ΔV V n ) are predicted in the prediction model. With continuous reading of real-time drilling data, the prediction model also predicts the state quantity in real time.

[0204] The above is the preferred embodiment of the present application. It should be noted that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, which should also be considered within the scope of protection of the present application.

Claims

1. A deep well overflow state perception method based on extended Kalman filter prediction, characterized in that, The method comprises the following steps: S1: establishing a state space model of a drilling wellbore and formation coupling flow system based on a bond graph principle; S2: establishing an observation equation model of the state space model of the drilling wellbore and formation coupling flow system by using real-time data of pressure before and after overflow, inlet and outlet flow, and mud pit incremental logging parameters; wherein, in the pressure before and after overflow, the standpipe pressure is used in the drilling circulation condition, and the casing pressure is used in the non-drilling circulation condition; S3: establishing a state equation model of the state space model of the drilling wellbore and formation coupling flow system by using a porous medium seepage theory and an oil and gas well fluid mechanics principle; S4: performing real-time prediction on the formation pressure and the wellbore and formation coupling flow state by introducing an extended Kalman filter prediction method; In step S1, the method for establishing the state space model of the drilling wellbore and formation coupling flow system based on the bond graph principle is as follows: In the state space model of the drilling wellbore and formation coupling flow system, a pump flow source with known pressure or flow is defined as Sf, and other external energy sources are defined as potential sources Se; the element of the mud tank is modeled as a capacitive element C; the pipeline filled with liquid is represented by an inertial element I, and the fluid friction and the pressure drop generated thereby are represented by a resistive element R; the mass conservation is modeled by a common potential junction 0 node, and the momentum conservation is modeled by a common flow junction 1 node; The state space model of the drilling wellbore and formation coupling flow system can be divided into a state space model of the drilling wellbore and formation coupling flow system during drilling circulation and a state space model of the drilling wellbore and formation coupling flow system during non-drilling circulation according to different working conditions; The bond graph of the state space model of the drilling wellbore and formation coupling flow system during drilling circulation comprises the following: A drilling fluid conveying channel from a drilling pump to a bottom hole is defined, including a ground pipeline, a drill string, and a drill bit water eye as a common flow junction 1; an annulus from the bottom hole to a ground drilling fluid outlet is defined as a common flow junction 2; a reservoir to the annulus is defined as a common flow junction 3; and a bottom hole gathered by the drill string water eye inflow, formation fluid invasion, and annulus upflow is defined as a common potential junction 0; The resistance element includes a drill pipe internal pressure drop coefficient Rrd and a drill bit local pressure drop coefficient Rdb, which respectively correspond to a drill string circulating pressure loss Prd and a drill bit local pressure drop Pdb; the inertia element includes a drill pipe internal drilling fluid inertia Id, which corresponds to a drill pipe internal drilling fluid momentum change rate The potential source includes a drill pipe internal drilling fluid liquid column potential source Se, which corresponds to a drill pipe internal drilling fluid liquid column pressure Pdh; the flow source includes a drilling pump pressure and displacement flow source Sf and a flow source Sf flowing out of the drill bit water hole, the drilling pump pressure and displacement flow source Sf corresponding to the pump pressure Pp and the drill pipe internal flow rate Qp, and the flow source Sf flowing out of the drill bit water hole corresponding to the bottom hole pressure Pbh and the drill pipe internal flow rate Qp; The potential source in the 2# co-flow junction from the annulus well bottom to the ground drilling fluid outlet includes the potential source Se of the drilling fluid column in the annulus, corresponding to the annulus fluid column pressure Pah; the resistive element includes the pressure drop coefficient Ra in the annulus and the throttle resistance coefficient Rc, corresponding to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the fluid inertia Ia in the annulus, corresponding to the annulus fluid momentum change rate The flow source includes the flow source Sf at the bottom of the annulus, corresponding to the flow rate Qa in the annulus and the well bottom pressure Pbh; In the common flow junction 3 from the reservoir to the annulus, the potential sources include a formation pressure potential source Se corresponding to a formation pore pressure Pf; the resistive elements include a porous medium seepage resistance coefficient Rf corresponding to a formation seepage pressure consumption Prf and a wellbore and formation interlayer flow Qf; and the flow sources include an inflow bottom hole flow source Sf corresponding to the wellbore and formation interlayer flow Qf and the bottom hole pressure Pbh; In the common potential junction 0, the flow sources include an outflow drill bit water eye flow source Sf, an annulus bottom flow source Sf, and an inflow bottom hole flow source Sf; Since a float valve is installed in the drill pipe, the drill pipe and the annulus are not connected during pump stopping, and the bond graph of the state space model of the drilling wellbore and formation coupling flow system during non-drilling circulation comprises the following: An annulus from the bottom hole to the ground drilling fluid outlet is defined as a common flow junction 4; a reservoir to the annulus is defined as a common flow junction 5; and a bottom hole gathered by the drill string water eye inflow, formation fluid invasion, and annulus upflow is defined as a common potential junction 0; 4# In the co-flow junction 1, the potential source includes the potential source Se of the drilling fluid column in the annulus, corresponding to the annulus fluid column pressure Pah; the resistive element includes the annulus pressure drop coefficient Ra and the throttle resistance coefficient Rc, corresponding to the annulus circulating pressure loss Pra and the casing pressure Pc respectively; the inertial element includes the fluid inertia Ia in the annulus, corresponding to the annulus fluid momentum change rate The flow source includes the flow source Sf at the bottom of the annulus, corresponding to the flow rate Qa in the annulus and the bottom hole pressure Pbh; 5#Common flow junction 1, potential source includes formation pressure potential source Se, corresponding to the formation pore pressure Pf; resistive elements include the seepage resistance coefficient Rf in the porous medium, corresponding to the formation seepage pressure Prf and the annulus flow Qf; flow source includes the flow source Sf into the well bottom, corresponding to the annulus flow Qf and the well bottom pressure Pbh; 2#Common potential junction 0, flow source includes the flow source Sf at the bottom of the annulus and the flow source Sf into the well bottom; According to the direction of the substance energy flow of the bond graph, combined with the law of conservation of mass and energy, the state space model of the coupling flow system of the drilling wellbore and the formation is established.

2. The deep well kick detection method based on extended Kalman filter prediction according to claim 1, 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 to characterize the situation that the pump pressure overcomes various circulating friction generated by the fluid flow in the wellbore in the process of drilling circulation drilling; the field drilling pump pressure is equivalent to the standpipe pressure without considering the surface pipeline circulating friction; considering the influence of formation pressure on pump pressure, the equation of pump pressure containing formation pressure is constructed, that is: P fr = P f - P bh P p = P f - P fr + P dr - P h during drilling cycles P c = P f - P fr - P ra - P ah , non-drilling circulation period where P p is pump pressure, Pa; P f is formation pressure, Pa; P fr is the differential between formation pressure and bottom hole pressure, Pa; P bh is bottom hole pressure, Pa; P dr is the frictional resistance to fluid flow in the wellbore drill pipe, Pa; P h is the hydrostatic column pressure of the fluid in the wellbore drill pipe, Pa, P c is casing pressure, Pa; P ra is annular circulating pressure loss, Pa; P ah is annular fluid column pressure, Pa.

3. The deep well kick detection method based on extended Kalman filter prediction according to claim 2, characterized in that, In step S2, the volume observation equation model is used to characterize the mud pit volume data observed by the drilling monitoring equipment, which is affected by the error of the field recording personnel and the monitoring equipment, and the observation equation model of the mud pit volume is as follows: V t = V m + V n In the formula, V t is the total volume of the mud pit, m 3 ; V m is the standard volume of the mud pit, m 3 ; V n is the volume change of the mud pit, m 3 .

4. The deep well kick detection method based on extended Kalman filter prediction according to claim 3, characterized in that, In step S2, the flow observation equation model is used to characterize the relationship between the fluid volume change in the wellbore annulus, which contains mass, flow rate and cross-sectional area physical parameters, and is related to the momentum physical quantity of the wellbore annulus in the state equation, so the equation of the outlet flow and the wellbore annulus momentum is constructed, wherein the definition of the wellbore annulus inertia coefficient is the mass change rate per unit area, considering that the cross-sectional area of the wellbore annulus is different, the wellbore annulus is divided into two sections to establish the equation, which are the open hole section and the casing section: Bare section: Casing segment: wherein Q o is the fluid flow rate of the annular open hole section, m 3 · s -1 ; Q c is the fluid flow rate of the annular casing section, m 3 · s -1 ; Γ o is the fluid momentum of the annular open hole section, kg·(m·s) -1 ; Γ c is the fluid momentum of the annular casing section, kg·(m·s) -1 ; I o is the fluid flow inertial coefficient of the annular open hole section, kg·m -4 ; I c is the fluid flow inertial coefficient of the annular casing section, kg·m -4 ; p is the annular fluid density, kg·m -3 ; H o is the vertical depth of the annular open hole section, m; H c is the vertical depth of the annular casing section, m; A o is the cross-sectional area of the annular open hole section, m 2 ; A c is the cross-sectional area of the annular casing section, m 2 ; In the actual drilling surface equipment monitoring, the subsection fluid flow Q o , Q c of the annulus of the open hole section and the casing section cannot be monitored, only the outlet flow at the wellhead is monitored, and the above subsection flow calculation is integrated considering that the characterization parameter in the observation equation is one of the drilling parameters and the continuity of the flow in the wellbore, that is: I a = I o + I c where Q a is the exit flow rate at the wellhead, m 3 · s -1 ; Γ a is the annulus fluid momentum, kg·(m·s) -1 ; I a is the total annulus fluid inertia coefficient, kg·m -4 ; The observation equation model is represented as: During drilling cycle During non-drilling circulation.

5. The deep well kick detection method based on extended Kalman filter prediction according to claim 4, wherein, In step S3, the state equation model includes: a wellbore and formation pressure difference change amount model, a wellbore annulus fluid momentum change amount model and a annulus fluid mass change amount model; In the wellbore and formation pressure difference change amount model, the formation pressure is only related to the depth and does not change with the drilling time and other parameters, and for unpredictable formations, the formation pressure changes with the depth has randomness, and its expression is as follows: wherein represents the formation pressure P f derivative with respect to time; In the wellbore annulus fluid momentum change amount model, according to the momentum conservation relationship of the fluid in the annulus, combined with the wellbore-formation coupling mechanics model, the total momentum change amount of the annulus drilling fluid is equal to the total of all forces applied to the fluid at the well bottom, and the fluid momentum equation of the wellbore annulus is as follows: wherein represents the annulus fluid momentum Γ a derivative with respect to time; In the annulus fluid mass change amount model, it is assumed that the annulus drilling fluid density is constant, and the mass change amount of the annulus fluid is only related to the volume change of the annulus fluid. Under normal drilling circulation drilling conditions, the mass of the drilling fluid entering and leaving the mud pit is conserved, that is, the volume change amount of the mud pit is constant. After the well kick occurs, the formation fluid invades the wellbore, causing the total mass of the fluid in the wellbore to increase, which destroys the original balance of the drilling fluid entering and leaving, and thus causes the volume of the mud pit to increase. Assuming that the drilling fluid density is constant, the mass change amount of the annulus fluid can be represented by the volume change amount of the drilling fluid pit, and its conservation equation is as follows: wherein V is the volume of the mud pit n Q is the derivative with respect to time a Q is the annulus outlet flow rate, m 3 · s -1 Q is the annulus outlet flow rate, m p Q is the drill pipe inlet flow rate, m 3 · s -1 · s In summary, the state equation model can be represented as:

6. The deep well kick detection method based on extended Kalman filter prediction according to claim 5, wherein, The step S4 comprises: S41: linearizing the state equation; S42: linearizing the observation equation; S43: discretizing the state equation linearized in the step S41; S44: predicting the wellbore and formation coupling flow state in real time by using the extended Kalman filter prediction method.

7. The deep well kick detection method based on extended Kalman filter prediction according to claim 6, wherein, In the steps S41 and S42: Supposing that the state variable x(t) is the change amount of the wellbore and formation pressure difference, the change amount of the wellbore annulus momentum and the mass change amount of the annulus fluid, the state equation of the wellbore and formation coupling flow system state space model is linearized by using the Taylor series expansion method, and then the linearized equation is as follows: f(x) represents a certain function; δ represents a change amount of a certain physical quantity; a 11 ~ a 33 is the matrix coefficient after linearization of the state equation; The observation equation is linearized by using the same method, that is, the Taylor series expansion method, the observation equation of the wellbore and formation coupling flow system state space model is linearized, and the linearized equation is as follows: where b 11 ~b 33 are the matrix coefficients after linearization of the observation equation.

8. The deep well kick detection method based on extended Kalman filter prediction according to claim 7, wherein, The specific process of the step S43 is as follows: The linear state differential matrix is discretized using inverse Laplace transformation, i.e., the linearized state matrix is discretized, and the obtained coefficient matrix is denoted as A d The discretized equation is as follows: wherein A d is a state transition matrix, x n is a state change at time n, x n-1 is a state change at time n-1. wherein A d = e At , In the formula, e is a natural constant, and t is the time interval between data points.

9. The deep well kick detection method based on extended Kalman filter prediction according to claim 8, wherein, The specific process of the step S44 is as follows: (1) preliminary prediction of the state variable at the time n x n (-) = A d x n-1 (+) where x n (-) is the preliminary predicted state quantity at time n, dimensionless; A d is the state transition matrix; x n-1 (+) is the modified predicted state quantity at time n-1, dimensionless, x n-1 (+) is the known quantity, using the x n (+) obtained in the previous step, with the initial value (2) preliminary prediction of the covariance transfer matrix at the time n P n (-) = A d P n-1 (+) A d T + Q n-1 where P n (-) is the preliminary covariance transfer matrix at time n; P n-1 (+) is the modified covariance transfer matrix at time n-1; P n-1 (+) is a known quantity, using the P n (+) of the previous step, with an initial value of the identity matrix Q n-1 represents the state model error matrix at time n-1; wherein G = [1 0 0] T T represents matrix transpose; is P f standard deviation of the normal distribution; (3) calculation of the Kalman gain at the time n where H n is the observation coefficient matrix, i.e. R n is the positive definite variance matrix of the system measurement noise, where are the standard deviations of the normal distribution of P p , V t , Q a , determined by the measurement system accuracy; (4) correction of the predicted state variable at the time n x n (+) = x n (-) + K n [z n -H n x n (-)] where x n (+) is the corrected predicted state quantity at time n, dimensionless; z n is the observation variable at time k, and (5) correction of the predicted covariance transfer matrix at the time n P n (+) = (I - K n H n )P n (-) (I - K n H n ) T + K n R n K n T where P n (+) is the covariance transition torque at time n, and I is the identity matrix. x n (+)、P n (+) as the last time parameter, repeat steps (1) ~ (5), x n (+) for the final prediction results According to the change of the time node, the formation pressure P f , wellbore annulus hydraulic momentum Г a , and the predicted mud pit increment V n .

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