CN111894561B - Stratum characteristic while-drilling interpretation method suitable for underbalanced drilling - Google Patents
Stratum characteristic while-drilling interpretation method suitable for underbalanced drilling Download PDFInfo
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Abstract
The invention relates to a stratum characteristic while-drilling interpretation method suitable for underbalanced drilling, which is used for performing stratum characteristic while-drilling interpretation by taking bottom hole pressure and liquid phase outlet flow as measurement parameters, wherein the determination process of the interpretation parameters comprises the following steps: acquiring basic parameters of a simulation well, and constructing an oil-gas-water three-phase variable mass flow model; constructing a state equation and a measurement equation of a shaft hydraulics system, wherein the state equation is established according to the interpretation parameters, and the measurement equation is established according to an oil-gas-water three-phase variable mass flow model; predicting, updating and correcting interpretation parameters based on an unscented Kalman filtering interpretation algorithm according to a state equation and a measurement equation to obtain values of the interpretation parameters; the method has the advantages that the formation pressure and permeability can be accurately predicted in real time in the drilling process, and the method has important theoretical and practical significance for improving the safety and timeliness of underbalanced drilling and later-stage well completion operation.
Description
Technical Field
The invention relates to the technical field of underbalanced drilling, in particular to a stratum characteristic while-drilling interpretation method suitable for underbalanced drilling.
Background
The underbalanced drilling refers to a drilling process in which low-density fluids such as gas, foam and aerated drilling fluid are used as circulating media, and the bottom of a well is in negative pressure difference. Because the bottom hole presents negative pressure difference, the underbalanced drilling is beneficial to improving the mechanical drilling speed, finding a reservoir and reducing the reservoir damage, thereby being widely applied. When the reservoir is opened in an underbalanced mode, the formation fluid can enter the shaft under the action of negative pressure difference, and further flow parameters such as shaft pressure and flow are changed. Due to the coupling effect between the shaft fluid and the stratum, stratum characteristic parameter values such as stratum pressure, permeability and the like can be obtained by monitoring the change of measurement parameters such as bottom pressure, outlet flow and the like, and further an underbalance drilling explanation while drilling theory is derived. Compared with the conventional cable logging interpretation method, the method has the advantages that the test pipe column is not required to be put in after the drilling is stopped, the reservoir information can be quickly acquired in normal drilling, and the method has important significance for reservoir early identification, well drilling risk reduction and well drilling time effectiveness improvement.
The existing stratum characteristic interpretation method mainly utilizes four measurement parameters of riser pressure, bottom hole pressure and gas phase and liquid phase outlet flow to carry out interpretation, and the more the measurement parameters are, the more the calculation amount and the time consumption are correspondingly increased. Second, existing studies have generally established an interpretation model of formation pressure and permeability based on L-M (Levenberg-Marquardt ) and EKF (Extended Kalman Filter). Among them, L-M is a non-recursive estimation algorithm, and all historical measurement data need to be used in calculation, so that it is not real-time. The EKF has prominent limitation, requires that a system is approximately linear, needs to calculate a complex Jacobian matrix, and is difficult to ensure the calculation precision and stability.
Disclosure of Invention
The invention provides a stratum characteristic while-drilling interpretation method suitable for underbalanced drilling aiming at the technical problems in the prior art, and solves the problems that in the prior art, the calculation amount is long in time consumption and the calculation result precision is difficult to guarantee.
The technical scheme for solving the technical problems is as follows: a stratum characteristic while-drilling interpretation method suitable for underbalanced drilling is characterized in that the stratum characteristic while-drilling interpretation is carried out by taking bottom hole pressure and liquid phase outlet flow as measurement parameters, and the determination process of interpretation parameters comprises the following steps:
step 2, constructing a state equation and a measurement equation of a shaft hydraulics system, wherein the state equation is established according to the interpretation parameters, and the measurement equation is established according to an oil-gas-water three-phase variable mass flow model;
and 3, predicting, updating and correcting the interpretation parameters based on an unscented Kalman filtering interpretation algorithm according to the state equation and the measurement equation to obtain the values of the interpretation parameters. .
The invention has the beneficial effects that: the method has the advantages that the formation pressure and the permeability can be accurately predicted in real time in the drilling process, and the method has important theoretical and practical significance for improving the safety and the timeliness of underbalanced drilling and later-stage well completion operation.
On the basis of the technical scheme, the invention can be further improved as follows.
Further, in the state equation and the measurement equation in the step 2, the interpretation parameter is represented by a state vector in a vector form, and the measurement parameter is represented by a measurement vector in a vector form;
the state equation represents the relation of the state vectors of adjacent time points, and the measurement equation represents the relation of the state vectors and the measurement vectors of the same time point.
Further, the state equation and the measurement equation are:
xk＝f(xk-1)+wk-1；
zk＝h(xk)+vk；
xkand xk-1State vectors at the time k and k-1 respectively, and f (-) is a nonlinear system state function; z is a radical ofkH (-) is the oil-gas-water three-phase variable mass flow model for measuring the vector; w is ak-1、vkRespectively, the process noise and the measurement noise at the corresponding time of the system.
Further, after obtaining the basic parameters of the simulation well in the step 1, the process of determining the oil-gas-water three-phase variable mass flow model is as follows:
step 101, establishing a control equation of an oil-gas-water three-phase variable mass flow model, wherein the control equation comprises an injected gas mass conservation equation, a drilling fluid mass conservation equation, a produced gas mass conservation equation, a produced oil mass conservation equation and an oil-gas-water three-phase momentum conservation equation;
102, discretizing the control equation;
103, establishing an auxiliary equation of oil-gas-water three-phase variable mass flow, wherein the auxiliary equation comprises the following steps: drift flow equation, PR state equation and formation seepage equation;
and 104, carrying out numerical calculation aiming at the oil-gas-water three-phase variable mass flow model, wherein the process of numerical calculation is a process of obtaining the measurement vector through the state vector.
Further, in step 102, discretizing the governing equation by using a four-point difference display format:
dividing the axial space grid into fixed step lengths; the time meshing is divided into two phases: before the gas is transported to a wellhead, a time step length of real-time change is obtained based on gas-liquid interface tracking; in the steady-state simulating process after the gas is moved to the wellhead, setting the time step length as a fixed value;
the first spatial derivative in the control equation adopts a first windward format, and the first time derivative adopts four-point central difference.
Further, the step 104 includes:
step 10401, estimating bottom hole pressure P at time k +10 k+1Bringing into the formation pressure p given in the simulation calculation of the previous momentrOr the formation permeability K;
step 10402, calculating invasion amount under given reservoir fluid components by combining the stratum seepage equation;
in step 10403, assume pressure P at node j at time k +1j k+1(0)Solving the physical parameters of the density and viscosity of the gas-phase and liquid-phase components by using the PR state equation;
step 10404, assume the gas phase volume fraction α at node j at time k +1j k+1(0)Calculating the component speeds of the gas-liquid phase by a mass conservation equation;
step 10405, calculating a new gas phase volume fraction α in combination with said drift flow equationj k+1Judging | αj k+1-αj k+1(0)|<If epsilon is true, executing a step 10406, otherwise returning to the step 10404 for re-iterative calculation, and epsilon is a threshold value set according to the precision requirement;
step 10406, substituting the known parameters into the momentum conservation equation, and calculating the pressure P at the new node j at the moment k +1j k+1If Pj k+1-Pj k+1(0)|<ε, description of Pj k+1(0)Estimating correctly, and taking the calculation parameter at the node j as the known quantity for calculating the j +1 point, otherwise, returning to the step 10403 for re-iterative calculation;
step 10407, the node is circulated to the wellhead all the time to obtain new wellhead back pressure Pc *If Pc *-Pc|<ε, description of Pc *And if the estimation is correct, continuing to calculate at the next moment, otherwise, returning to the step 10401.
Further, the step 3 comprises:
step 301, setting the state vector and the error covariance matrix at the initial moment;
step 302, according to the selected proportional correction symmetric sampling strategy, predicting the mean value and the error covariance matrix of the state vector at the current moment by the estimated value and the error covariance matrix of the state vector at the previous moment;
step 303, transmitting a Sigma point by using a measurement equation, and predicting a value of a measurement vector, an autocovariance matrix and a cross covariance matrix at the current moment;
and step 304, correcting and updating the mean value and the error covariance matrix of the state vector at the current moment by using the value of the measurement vector at the current moment, the autocovariance matrix and the cross covariance matrix predicted in the step 303.
Further, the step 302 includes:
30201, estimating the state vector from the previous time
Sum error covariance matrix Pk-1To calculate Sigma point xi,k-1Weight W for mean weightingi (m)Weight W used for sum covariance weightingi (c)：
Wherein λ is a scale factor, λ ═ α2(n + κ) -n; n is the dimension of the state vector; kappa is an adjustable parameter, and for Gaussian distribution, when n is less than or equal to 3, taking kappa as 3-n, when n is equal to>Taking kappa as 0; alpha is a spreading factor, affecting the Sigma point around
The distribution state of (1) is in the range of[0,1](ii) a Beta is a parameter for describing prior distribution information of the state vector, and for Gaussian distribution, the optimal value is 2;
step 30202, using the equation of state to transfer the Sigma point as xi,k/k-1：
xi,k/k-1＝f(xi,k-1)i＝0,1,…,2n。
30303 predicting the state mean value of the current time
Sum covariance matrix Pk/k-1：
Wherein Q isk-1Is the process noise covariance matrix at the previous time instant.
Further, in step 303, a measurement equation is used to transfer a Sigma point as zi,k/k-1：zi,k/k-1＝h(xi,k-1)i＝0,1,…,2n；
Predicting the value of a measurement vector at the current time
Auto-covariance matrix
Sum cross covariance matrix
The formula of (1) is as follows:
wherein R iskThe noise covariance matrix is measured for the current time instant.
Further, the step 304 includes:
30401, computing a Kalman gain matrix K according to the autocovariance matrix and the cross-covariance matrixk：
Step 30402, based on the value of the measurement vector at the current time obtained in step 303, averaging the state vector at the current time
Sum error covariance matrix PkAnd (3) correction updating:
the beneficial effect of adopting the further scheme is that: by applying the unscented Kalman filtering technology, the underground pressure and the outlet flow can be corrected and calculated in real time, the application range of the traditional shaft hydraulics is expanded, and the utilization rate and the prediction precision of the measurement data stream are improved; the reservoir pressure or permeability can be predicted in real time, accurate quantitative analysis of key stratum parameters is realized, and important references are provided for safe and efficient drilling and subsequent well completion operation.
Drawings
FIG. 1 is a schematic diagram of an embodiment of a gas injection underbalanced drilling system for a drill string;
FIG. 2 is a flow chart of a formation characteristic while drilling interpretation method suitable for underbalanced drilling according to an embodiment of the present invention;
FIG. 3 is a flow chart of an embodiment of determining an oil-gas-water three-phase variable mass flow model provided by the present invention;
FIG. 4 is a flow chart of an embodiment of an unscented Kalman filter based interpretation algorithm provided by the present invention;
in the drawings, the components represented by the respective reference numerals are listed below:
1. slurry pump, 2, vertical pressure gauge, 3, PWD, 4, sleeve pressure gauge, 5, throttle valve, 6, gas-liquid separator, 7, liquid phase flowmeter, 8, gas phase flowmeter, 9 and gas injection pipeline.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth by way of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, which is a schematic structural diagram of an embodiment of a gas injection underbalanced drilling system of a drill string, it can be known from fig. 1 that the gas injection underbalanced drilling process of the drill string includes the following specific steps: the gas is mixed with the drilling fluid pumped by the mud pump 1 through the gas injection line 9 and is injected into the drill string together to the bottom drill bit. With the opening of the reservoir section during drilling, the formation gas-liquid fluid gradually enters the wellbore and returns up to the wellhead together with the injected gas-liquid fluid. The gas-liquid separator 6 is arranged on the ground to finally separate the gas phase from the liquid phase, and the casing pressure gauge 4 and the throttle valve 5 are respectively used for measuring the casing pressure and controlling the flow rate.
In the existing research, the riser pressure shown in the vertical pressure table 2, the bottom hole pressure measured by the PWD (pressure while drilling) 3, and the gas phase and liquid phase outlet flow read by the liquid phase flowmeter 7 and the gas phase flowmeter 8 after passing through the gas-liquid separator 6 are often selected as measurement parameters. However, according to the U-tube principle, it is known that the bottom hole pressure and the riser pressure can build a pressure transfer relationship within the drill string. In addition, the gas-liquid phase outlet flow rate has an intuitive mathematical relationship in a shaft-stratum coupled flow system, and the gas-liquid phase outlet flow rate is equal to the sum of the inlet flow rate, the stratum seepage flow rate and the gas expansion rate according to the superposition principle without considering gas-liquid mass transfer. Therefore, the measurement parameters can be simplified into two types of bottom hole pressure and liquid phase outlet flow.
As shown in fig. 2, which is a flowchart of a formation characteristic while drilling interpretation method suitable for underbalanced drilling according to an embodiment of the present invention, a formation characteristic while drilling interpretation is performed by using a bottom hole pressure and a liquid phase outlet flow as measurement parameters, and a determination process of the interpretation parameters includes:
And 2, constructing a state equation and a measurement equation of the shaft hydraulics system, wherein the state equation is established according to the interpretation parameters, and the measurement equation is established according to an oil-gas-water three-phase variable mass flow model.
And 3, predicting, updating and correcting the interpretation parameters based on the unscented Kalman filtering interpretation algorithm according to the state equation and the measurement equation to obtain the values of the interpretation parameters.
The invention provides a stratum characteristic while-drilling interpretation method suitable for underbalanced drilling, which combines an unscented Kalman filtering technology with an oil-gas-water three-phase variable mass flow model, utilizes the relation between measurement parameters to simplify the original four measurement parameters into two types of bottom hole pressure and liquid phase outlet flow, can predict the stratum pressure or the stratum permeability in real time aiming at the process of drilling a reservoir in an underbalanced mode, and can realize accurate quantitative interpretation and analysis of the reservoir characteristic parameters.
Example 1
In the embodiment, the formation characteristic while drilling interpretation is carried out by using bottom hole pressure and liquid phase outlet flow as measurement parameters z, and the interpretation parameters x comprise formation pressure and formation permeability.
Specifically, the measurement parameter z and the interpretation parameter x can be expressed as:
z＝[P0(tk),qout,1(tk)]T,x＝[K(tk),pr(tk)]T。
wherein K represents the formation permeability, prRepresenting the formation pressure, P0Representing the bottom hole pressure, qout,1Denotes the liquid phase outlet flow rate, tkAnd k time points corresponding to the measured data are shown.
The determination process of the interpretation parameter x includes:
Specifically, the basic parameters include: well depth, well bore structure, drilling tool assembly, displacement, drilling fluid density, drilling fluid rheological parameters, formation temperature, geothermal gradient, gas injection quantity, drilling rate, formation porosity, skin factor and the like.
And 2, constructing a state equation and a measurement equation of the shaft hydraulics system, wherein the state equation is established according to the interpretation parameters, and the measurement equation is established according to an oil-gas-water three-phase variable mass flow model.
Preferably, in the state equation and the measurement equation, the state vector in the form of a vector represents the interpretation parameter, the measurement vector in the form of a vector represents the measurement parameter, the standard deviation of the state noise and the measurement noise is set by combining the parameter attributes when the state equation and the measurement equation are constructed, the state equation represents the relationship between the state vectors of adjacent time points, and the measurement equation represents the relationship between the state vector of the same time point and the measurement vector.
Specifically, the state equation and the measurement equation can be expressed as:
xk＝f(xk-1)+wk-1；
zk＝h(xk)+vk。
in the formula: x is the number ofkAnd xk-1State vectors at the time k and k-1 respectively, and f (-) is a nonlinear system state function; z is a radical ofkH (-) is an oil-gas-water three-phase variable mass flow model for measuring vectors; w is ak-1、vkRespectively corresponding to the process noise and the measurement noise at the moment of the system, and both satisfy the zero-mean white Gaussian noise distribution wk～N{0,QkAnd vk～N{0,RkMutually exclusiveAnd off.
Specifically, a flowchart of an embodiment of determining the oil-gas-water three-phase variable mass flow model h (-) is shown in fig. 3, and as can be seen from fig. 3, after the basic parameters of the simulation well are obtained in step 1, a process of determining the oil-gas-water three-phase variable mass flow model may be as follows:
step 101, comprehensively applying a shaft multiphase flow and seepage flow mechanics theory to establish a control equation of an oil-gas-water three-phase variable mass flow model.
Specifically, the control equation comprises an injected gas mass conservation equation, a drilling fluid mass conservation equation, a produced gas mass conservation equation, a produced oil mass conservation equation and an oil-gas-water three-phase momentum conservation equation.
The conservation of mass equation of the injected gas is as follows:
the drilling fluid mass conservation equation is as follows:
the produced gas mass conservation equation is as follows:
the produced oil mass conservation equation is as follows:
the oil-gas-water three-phase momentum conservation equation is as follows:
in the formula (I), the compound is shown in the specification,
is a partial derivative of the time,
is the partial derivative of axial displacement, A is the area of annular flow channel, and the unit is m2；ρg，ρl，ρoThe density of gas phase, drilling fluid and oil phase is respectively, and the unit is kg/m3；αg，αl，αoThe volume fractions of gas phase, drilling fluid and oil phase are respectively, and are dimensionless; v. ofg，vl，voThe actual flow rates of the gas phase, the drilling fluid and the oil phase are respectively, and the unit is m/s; x is the number ofig，xfgThe mass fractions of the injected gas and the produced gas are respectively dimensionless; q. q.sfg，qoThe penetration rates of the gas phase and the oil phase are respectively unit thickness, and the unit is kg/(s.m); g is gravity acceleration, and is 9.81m/s2(ii) a Theta is an included angle between the well hole and the horizontal direction; p is a radical offIs the on-way pressure drop in Pa; p is a radical ofacAcceleration drop is given in Pa.
And 102, discretizing the control equation.
Specifically, the control equation may be discretized in a four-point difference display format:
the axial space grid is divided into fixed step length, and the time grid is divided into two stages: before the gas is transported to a wellhead, the time step length of real-time change is obtained based on gas-liquid interface tracking; in the quasi-steady state process after the gas moves to the wellhead, the time step is set to a certain value. The first spatial derivative in the control equation adopts a first windward format, and the first time derivative adopts four-point central difference, so that the model is discretized according to the principle.
The axial nodes are j and j +1 from bottom to top, and the time nodes are k and k +1 from front to back.
And 103, establishing an auxiliary equation of oil-gas-water three-phase variable mass flow.
The model cannot be solved by only relying on the control equations of the multiphase flow model, and in order to further form a closed equation system, the following auxiliary equations are considered, and specifically, the auxiliary equations comprise: drift flow equation, flow pattern discrimination equation, annular pressure loss equation, PR state equation and stratum seepage equation.
And 104, performing numerical calculation on the oil-gas-water three-phase variable mass flow model, wherein the numerical calculation process is a process of obtaining a measurement vector through a state vector.
Specifically, the calculation method comprises the following steps:
specifically, step 104 includes:
step 10401, estimating bottom hole pressure P at time k +10 k+1Simultaneously bringing the formation pressure p given in the simulation calculation of the previous momentrOr formation permeability K.
Step 10402, calculating invasion volume for the given reservoir fluid composition in combination with the formation permeability equation.
In step 10403, assume pressure P at node j at time k +1j k+1(0)And solving physical parameters such as density, viscosity and the like of the gas-phase and liquid-phase components by using a PR state equation.
Step 10404, assume the gas phase volume fraction α at node j at time k +1j k+1(0)And calculating the component speeds of the gas phase and the liquid phase by a mass conservation equation.
Step 10405, calculating new gas phase volume fraction α in combination with drift flow equationj k+1Judging | αj k+1-αj k+1(0)|<If epsilon is true, executing the step 10406, otherwise returning to the step 10404 to repeat the calculation, and epsilon is a threshold value set according to the precision requirement.
Step 10406, substituting the known parameters into the momentum conservation equation, and calculating the pressure P at the new node j at the moment k +1j k +1If Pj k+1-Pj k+1(0)|<ε, description of Pj k+1(0)And (4) estimating correctly, taking the calculation parameter at the node j as a known quantity for calculating the point j +1, and otherwise, returning to the step 10403 to carry out repeated iterative calculation until the precision requirement is met.
10407, circulating the node to the wellhead to obtain a new wellhead back pressure Pc *If Pc *-Pc|<ε, description of Pc *And if the estimation is correct, the calculation is continued at the next moment, otherwise, the step 10401 is returned.
And 3, predicting, updating and correcting the interpretation parameters based on the unscented Kalman filtering interpretation algorithm according to the state equation and the measurement equation to obtain the values of the interpretation parameters.
As shown in fig. 4, which is a flowchart of an unscented kalman filter-based interpretation algorithm provided by the present invention, as can be seen from fig. 4, preferably, step 3 may include:
step 301, setting a state vector and an error covariance matrix at an initial time.
And step 302, according to the selected proportional correction symmetric sampling strategy, predicting the mean value and the error covariance matrix of the state vector at the current moment by the estimated value and the error covariance matrix of the state vector at the previous moment.
The step 302 is to update the value of the state vector, specifically, the step 302 includes:
30201, estimating the state vector from the previous time
Sum error covariance matrix Pk-1To calculate Sigma point xi,k-1Weight W for mean weightingi (m)Weight W used for sum covariance weightingi (c)：
Wherein λ is a scale factor, λ ═ α2(n + κ) -n; n is the dimension of the state vector; kappa is an adjustable parameter, and for Gaussian distribution, when n is less than or equal to 3, taking kappa as 3-n, when n is equal to>Taking kappa as 0; alpha is a spreading factor, affecting the Sigma point around
The distribution state of (2) generally takes the value of [0,1](ii) a Beta is a parameter describing prior distribution information of the state vector, and for Gaussian distribution, the optimal value is 2.
Step 30202, using equation of state to transfer the Sigma point as xi,k/k-1：
xi,k/k-1＝f(xi,k-1)i＝0,1,…,2n。
30303 predicting the state mean value of the current time
Sum covariance matrix Pk/k-1：
Wherein Q isk-1Is the process error covariance matrix at the previous time instant.
Step 303, transmitting the Sigma point by using a measurement equation, and predicting the value of the measurement vector, the autocovariance matrix and the cross covariance matrix at the current moment.
This step 303 is an update of the value of the measurement vector, specifically, in step 303:
using the measurement equation to deliver the Sigma point as zi,k/k-1：zi,k/k-1＝h(xi,k-1)i＝0,1,…,2n。
Predicting the value of a measurement vector at the current time
Auto-covariance matrix
Sum cross covariance matrix
The formula of (1) is:
wherein R iskIs the covariance matrix of the measurement error at the current time.
And step 304, correcting and updating the mean value and the error covariance matrix of the state vector at the current moment by using the value of the measurement vector at the current moment, the autocovariance matrix and the cross covariance matrix predicted in the step 303.
The step 304 is a correction updating process of the mean value of the state vector, which specifically includes:
30401, computing a Kalman gain matrix K according to the autocovariance matrix and the cross-covariance matrixk：
Step 30402, baseThe value of the measurement vector at the current time obtained in step 303, the mean value of the state vector at the current time
Sum error covariance matrix PkAnd (3) correction updating:
the above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (6)
1. A stratum characteristic while-drilling interpretation method suitable for underbalanced drilling is characterized in that the method utilizes bottom hole pressure and liquid phase outlet flow as measurement parameters to carry out stratum characteristic while-drilling interpretation, and the determination process of the interpretation parameters comprises the following steps:
step 1, obtaining basic parameters of a simulation well, and constructing an oil-gas-water three-phase variable mass flow model;
step 2, constructing a state equation and a measurement equation of a shaft hydraulics system, wherein the state equation is established according to the interpretation parameters, and the measurement equation is established according to an oil-gas-water three-phase variable mass flow model;
step 3, predicting, updating and correcting the interpretation parameters based on an unscented Kalman filtering interpretation algorithm according to the state equation and the measurement equation to obtain values of the interpretation parameters;
in the state equation and the measurement equation in the step 2, the state vector in the form of a vector represents the interpretation parameter, and the measurement vector in the form of a vector represents the measurement parameter;
the state equation represents the relationship of the state vectors of adjacent time points, and the measurement equation represents the relationship of the state vectors and the measurement vectors at the same time point;
after obtaining the basic parameters of the simulation well in the step 1, the process of determining the oil-gas-water three-phase variable mass flow model is as follows:
step 101, establishing a control equation of an oil-gas-water three-phase variable mass flow model, wherein the control equation comprises an injected gas mass conservation equation, a drilling fluid mass conservation equation, a produced gas mass conservation equation, a produced oil mass conservation equation and an oil-gas-water three-phase momentum conservation equation;
102, discretizing the control equation;
103, establishing an auxiliary equation of oil-gas-water three-phase variable mass flow, wherein the auxiliary equation comprises the following steps: drift flow equation, PR state equation and formation seepage equation;
104, performing numerical calculation on the oil-gas-water three-phase variable mass flow model, wherein the numerical calculation process is a process of obtaining the measurement vector through the state vector;
in the step 102, a four-point difference display format is adopted to discretize the control equation:
dividing the axial space grid into fixed step lengths; the time grid is divided into two phases: before the gas is transported to a wellhead, a time step length of real-time change is obtained based on gas-liquid interface tracking; in the steady-state simulating process after the gas is moved to the wellhead, setting the time step length as a fixed value;
the first-order spatial derivative in the control equation adopts a first-order windward format, and the first-order time derivative adopts four-point central difference;
the step 104 comprises:
step 10401, estimating bottom hole pressure P at time k +10 k+1Bringing into the formation pressure p given in the simulation calculation of the previous momentrAnd formation permeability K;
step 10402, calculating invasion amount under given reservoir fluid components by combining the stratum seepage equation;
in step 10403, assume pressure P at node j at time k +1j k+1(0)Solving the physical parameters of the density and viscosity of the gas-phase and liquid-phase components by using the PR state equation;
step 10404, assume the gas phase volume fraction α at node j at time k +1j k+1(0)Calculating the component speeds of the gas phase and the liquid phase by a mass conservation equation;
step 10405, calculating a new gas phase volume fraction α in combination with said drift flow equationj k+1Judging | αj k+1-αj k+1(0)|<If epsilon is true, executing a step 10406, otherwise returning to the step 10404 for re-iterative calculation, and epsilon is a threshold value set according to the precision requirement;
step 10406, substituting the known parameters into the momentum conservation equation, and calculating the pressure P at the new node j at the moment k +1j k+1If Pj k+1-Pj k+1(0)|<ε, description of Pj k+1(0)Estimating correctly, and taking the calculation parameter at the node j as the known quantity for calculating the j +1 point, otherwise, returning to the step 10403 for re-iterative calculation;
10407, circulating the node to the wellhead to obtain a new wellhead back pressure Pc *If Pc *-Pc|<ε, description of Pc *And if the estimation is correct, continuing to calculate at the next moment, otherwise, returning to the step 10401.
2. The method of claim 1, wherein the state equation and measurement equation are:
xk＝f(xk-1)+wk-1；
zk＝h(xk)+vk；
xkand xk-1State vectors at the time k and k-1 respectively, and f (-) is a nonlinear system state function; z is a radical ofkH (-) is the oil-gas-water three-phase variable mass flow model for measuring the vector; w is ak-1、vkRespectively, process noise and measurement noise at the corresponding moment of the system.
3. The method of claim 1, wherein step 3 comprises:
step 301, setting the state vector and the error covariance matrix at the initial moment;
step 302, according to the selected proportional correction symmetric sampling strategy, predicting the mean value and the error covariance matrix of the state vector at the current moment by the estimated value and the error covariance matrix of the state vector at the previous moment;
step 303, transmitting a Sigma point by using a measurement equation, and predicting a value of a measurement vector, an autocovariance matrix and a cross covariance matrix at the current moment;
and step 304, correcting and updating the mean value and the error covariance matrix of the state vector at the current moment by using the value of the measurement vector at the current moment, the autocovariance matrix and the cross covariance matrix predicted in the step 303.
4. The method of claim 1, wherein the step 302 comprises:
30201, estimating the state vector from the previous time
Sum error covariance matrix Pk-1To calculate Sigma point xi,k-1Weight W for mean weightingi (m)Weight W used for sum covariance weightingi (c)：
Wherein λ is a scale factor, λ ═ α2(n + κ) -n; n is the dimension of the state vectorCounting; kappa is an adjustable parameter, and for Gaussian distribution, when n is less than or equal to 3, taking kappa as 3-n, when n is equal to>Taking kappa as 0; alpha is an expansion factor and influences the distribution state of Sigma points around x, and the value range is [0, 1%](ii) a Beta is a parameter for describing prior distribution information of the state vector, and for Gaussian distribution, the optimal value is 2;
step 30202, using the equation of state to transfer the Sigma point as xi,k/k-1：
xi,k/k-1＝f(xi,k-1) i＝0,1,…,2n；
30303 predicting the state mean value of the current time
Sum covariance matrix Pk/k-1：
Wherein Q isk-1Is the process noise covariance matrix at the previous time instant.
5. The method of claim 1, wherein in step 303, a measurement equation is used to transfer the Sigma point as zi,k/k-1：zi,k/k-1＝h(xi,k-1)i＝0,1,…,2n；
Predicting the value of a measurement vector at the current time
Auto-covariance matrix
Sum cross covariance matrix
The formula of (1) is:
wherein R iskThe noise covariance matrix is measured for the current time instant.
6. The method of claim 1, wherein the step 304 comprises:
30401, computing a Kalman gain matrix K according to the autocovariance matrix and the cross-covariance matrixk：
Step 30402, based on the value of the measurement vector at the current time obtained in step 303, averaging the state vector at the current time
Sum error covariance matrix PkAnd (3) correction updating:
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