Deep well gas cut stratum parameter inversion method and system based on gas-liquid two-phase flow model

Abstract

The invention discloses a deep well gas cut stratum parameter inversion method and system based on a gas-liquid two-phase flow model, and the method comprises the steps: firstly building a gas-liquid two-phase flow model based on a shaft flow equation, and carrying out the discrete solving of a mathematical model through a finite difference algorithm; and then an unscented Kalman filter (UKF) is combined to construct an inversion model of formation parameters, and the formation pressure and the production index in the gas cut process are inverted by using the measurement data of the difference between the riser pressure and the liquid inlet and outlet flow. According to the stratum parameter inversion method provided by the invention, the stratum parameters can be accurately inverted, a basis is provided for accurate prediction and effective control of gas cut, and the application prospect is wide.

Description

Technical Field

[0001] The invention belongs to the technical field of oil and gas field drilling, and in particular relates to a deep well gas invasion formation parameter inversion method and system based on a gas-liquid two-phase flow model. Background Art

[0002] During the drilling of deep and ultra-deep wells, gas invasion is prone to occur due to the high temperature, high pressure, high stress and complex formation environment. If the gas invasion is not discovered in time and handled improperly, the continuous invasion of formation gas and the upward migration and expansion of gas in the wellbore will displace more drilling fluid in the wellbore, causing the wellbore pressure to continue to decrease, and the gas invasion rate will also increase. This vicious cycle will increase the risk of well control and even cause vicious blowout accidents. Effective control of wellbore pressure is the key to ensuring the safe implementation of well control measures, and accurate characterization of complex wellbore flow characteristics and pressure evolution is the prerequisite for predicting and controlling wellbore pressure. Therefore, accurate simulation and prediction of multiphase flow characteristics in the wellbore after gas invasion are crucial for safe and efficient drilling.

[0003] The Chinese patent CN202410794778.8 discloses a direct-push well-killing modeling method based on formation parameter inversion, including real-time acquisition of actual wellhead overflow data, actual drilling trajectory data, well depth structure data, and drill tool assembly data; pre-processing the wellhead overflow data, actual drilling trajectory data, well depth structure data, and drill tool assembly data respectively; and establishing a direct-push well-killing model based on the mass conservation equation and the drift flow model in combination with the gas-liquid two-phase flow model. An overflow simulation model is used to simulate the change of wellhead overflow volume over time during the overflow period, and then an ant colony search algorithm is used to obtain the actual wellhead overflow data as a comparison to invert the gas production index and formation pressure. This method requires a lot of real-time data and requires pre-processing of the data, so the preliminary work is relatively complicated.

[0004] The Chinese patent CN202410590140.2 discloses a method for ultra-deepwater drilling fracture morphology prediction and formation pressure inversion. The formation parameters are inverted by gas flow and riser pressure, and the mathematical expression is obtained by simulation to perform fracture width inversion. Then, according to the correlation between the fractures, the corresponding permeability calculation formula is obtained to perform formation parameter inversion. And using the iteration method, the permeability iteration formula is obtained to perform permeability inversion. At the same time, the formation porosity is calculated, and the fracture length is inverted according to the relationship between the fracture porosity and the fracture width and fracture length. This method mainly inverts the formation pressure, fracture length and width, and permeability, and does not involve the production index.

[0005] Based on the managed pressure drilling system, Habib et al. input the measured pump pressure and throttling pressure into the unscented Kalman filter estimator to simultaneously estimate the drill bit flow and gas inflow, and verified the robustness of the method using experimental and field data. However, this method is based on isothermal conditions, which is inconsistent with actual high temperature and high pressure well conditions.

[0006] Sun et al. established a pore pressure inversion model for gas invasion based on the mutual coupling between the wellbore and the formation and the changes in the volume and pressure of the annular gas caused by the movement and expansion of bubbles in the wellbore, and proposed a fast search algorithm to reduce the impact of measurement noise on the results. However, this method mainly focuses on inverting a single formation parameter, namely, formation pressure, formation permeability, etc., while the remaining formation parameters are mostly known hypothetical values.

[0007] In summary, the existing inversion methods of formation parameters need to be based on complex real-time wellbore data or set hypothetical values. However, in the actual drilling process, the parameters of high-pressure gas layers are often unknown, which makes the current inversion methods have certain limitations. Therefore, in order to clarify the evolution law of gas-liquid two-phase flow in deep well gas invasion wellbore, improve the prediction accuracy of wellbore pressure, and achieve safe and efficient treatment of gas invasion, it is necessary to solve the key problem of "inversion of formation parameters based on the fusion of gas-liquid two-phase flow mechanism model and time series data in gas invasion wellbore". Summary of the invention

[0008] In order to solve the technical problems existing in the background technology, the present invention aims to provide a deep well gas invasion formation parameter inversion method and system based on a gas-liquid two-phase flow model, which provides a reliable basis for monitoring and controlling gas invasion caused by high temperature, high pressure and complex formation environment in deep well drilling.

[0009] In order to solve the technical problem, the technical solution of the present invention is:

[0010] A deep well gas invasion formation parameter inversion method based on a gas-liquid two-phase flow model, the method comprising:

[0011] A wellbore flow model is established, and the model is discretely solved using the finite difference algorithm. An inversion model of formation parameters is constructed by combining the unscented Kalman filter (UKF), and the formation pressure and production index during gas invasion are inverted using the measured data of riser pressure and liquid inlet and outlet flow rate difference.

[0012] Furthermore, a wellbore flow model is established, including:

[0013] The first step is to build a gas-liquid two-phase flow control model in the annulus:

[0014] First, the model ignores the cross-sectional velocity distribution, the temperature gradient is linear, and the influence of drilling cuttings is not considered. Then the following equations are established: the drilling fluid mass conservation equation, the intruding gas mass conservation equation, and the gas-liquid mixture momentum conservation equation;

[0015] The drilling fluid mass conservation equation is:

[0016]

[0017] Where: a is the drilling fluid density in the annulus, kg / m 3 ; α l is the drilling fluid volume fraction, dimensionless; v l is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of ​​the annulus, m 2 ;

[0018] The mass conservation equation of the intruding gas is:

[0019]

[0020] Where: g is the gas density, kg / m 3 ; α g is the gas phase volume fraction, dimensionless; v g is the gas velocity, m / s;

[0021] The mixture momentum conservation equation is:

[0022]

[0023] Where: g is the acceleration due to gravity, 9.81m / s 2 ;P a is the annulus pressure, Pa; θ is the wellbore inclination, ° (starting from the vertical direction); F f is the friction pressure drop per unit length, Pa / m;

[0024] The sum of the drilling fluid volume fraction and the invading gas volume fraction is 1:

[0025] α g +α l =1 (4)

[0026] In the drift flow equation, the gas phase velocity can be expressed as:

[0027] v g =C0(v g α g +v l α l )+v gr (5)

[0028] Where: C0 is the slip coefficient; v gr is the slip velocity, m / s;

[0029] The slip coefficient and slip velocity can be expressed as:

[0030]

[0031] Where: A is the gas phase distribution coefficient in the liquid; γ is the reduction term of the slip coefficient; v c is the characteristic speed, m / s;

[0032] According to the PVT model, the density of gas can be expressed as:

[0033]

[0034] Where M g is the gas molar mass, kg / mol; R is the gas constant, J / mol / K; Z is the gas deviation factor, calculated using the following formula:

[0035]

[0036] In the formula, A1~A 11 is the coefficient; T r is the comparative temperature, dimensionless; ρ r For comparison density, dimensionless;

[0037] The second step is to construct the control equation of the single-phase flow of liquid in the drill pipe:

[0038] The governing equations of the single-phase flow of liquid in the drill pipe include two equations: the drilling fluid mass conservation equation and the drilling fluid momentum conservation equation;

[0039] The drilling fluid mass conservation equation is:

[0040]

[0041] Where: d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the cross-sectional area of ​​the drill pipe, m 2 ;

[0042] The momentum conservation equation in the drill pipe is:

[0043]

[0044] Where: P d D is the drilling fluid pressure in the pipe, Pa; d is the inner diameter of the drill pipe, m;

[0045] The third step is to construct the auxiliary equation:

[0046] The momentum conservation equation, i.e. the friction pressure drop per unit length F in Equation 3 and Equation 11 f The calculation formula is:

[0047]

[0048] Where: F f is the friction pressure drop per unit length, Pa / m; f is the Moody friction factor; D is the flow channel diameter, the inner diameter of the pipe in the drill pipe; the hydraulic diameter in the annulus, m; ρ is the density, kg / m 3 ; v is the fluid velocity, m / s;

[0049] The Moody friction factor f in formula (12) takes into account the influence of wall roughness and can be obtained by the following formula:

[0050]

[0051] Where Re is the Reynolds number;

[0052] In the gas-liquid two-phase flow model of gas invasion, equation (14) is used to define the relationship between the gas invasion rate, production index and formation pressure;

[0053] q g =J(P e -P b ) (14)

[0054] In the formula, q g is the gas invasion rate, kg / s; J is the production index, kg / s / MPa; P e is the formation pressure, MPa; P b is the bottom hole pressure, MPa, P b It can be calculated using the gas-liquid two-phase flow model.

[0055] Further, the discrete solution of the model using the finite difference algorithm specifically includes:

[0056] The entire wellbore is discretized into N nodes, and the flow control equations of the wellbore-formation system are solved using the finite difference method;

[0057] The annular flow equation is expressed as:

[0058]

[0059] Wherein, variables W, F(W) and Q(W) are functions of density, velocity, volume fraction and pressure; j = 1, 2 represent the mass conservation equations of liquid and gas phases; j = 3 represents the momentum conservation equation of gas-liquid two phases;

[0060] The mass conservation equation is expressed as:

[0061]

[0062] Furthermore, during the gas invasion process, the difference in surface inlet and outlet flow and the riser pressure can be measured; the formation pressure and production index during the gas invasion process are inverted using the measured data of the difference in inlet and outlet flow and the riser pressure;

[0063] The inlet and outlet flow difference of the ground at different times is the inlet and outlet flow difference of the liquid single-phase flow, which is expressed as:

[0064] Δq(t)=[Δq(t1),Δq(t2),…,Δq(t N )] (17)

[0065] Δq(t)=q out (t)-q in (t) (18)

[0066] Where t is time, s; Δq is the flow difference between the inlet and outlet of the liquid, m 3 / min;q out is the liquid outlet flow difference, m 3 / min;q in is the liquid inlet flow difference, m 3 / min;

[0067] The riser pressure data measured at different times are expressed as:

[0068] P sp (t) = [P sp (t1),P sp (t2),…,P sp (t N )] (19)

[0069] Where P sp is the standpipe pressure, MPa;

[0070] Taking formation pressure and production index as inversion parameters, the inversion parameters at different times are:

[0071] P e (t) = [P e (t1),P e (t2),…,P e (t N )] (20)

[0072] J(t)=[J(t1),J(t2),…,J(t N )] (twenty one)

[0073] Where P e is the formation pressure, MPa; J is the production index, kg / s / MPa;

[0074] Combined with the UKF algorithm, the formation pressure and production index are taken as state values, the inlet and outlet flow difference and the standpipe pressure are taken as observation values, and the state variable (X) and observation variable (Z) in the inversion model are expressed as follows:

[0075] X(k)=[P e (k),J(k)] T (twenty two)

[0076] Z(k)=[Δq(k),P sp (k)] T (twenty three)

[0077] The state model f(·) for formation parameter inversion using UKF algorithm is expressed as:

[0078] X(k)=X(k-1)+W(k) (24).

[0079] A deep well gas invasion formation parameter inversion system based on a gas-liquid two-phase flow model, the system comprising:

[0080] Wellbore flow modeling module, used to establish wellbore flow model;

[0081] A finite difference discretization module is used for discretizing and solving the wellbore flow model based on the established wellbore flow model by using a finite difference algorithm;

[0082] Unscented Kalman filter inversion module, used to build an inversion model of formation parameters in combination with unscented Kalman filter UKF;

[0083] The data fusion and inversion module is used to invert the formation pressure and production index during the gas invasion process using the measured data of the riser pressure and the liquid inlet and outlet flow difference.

[0084] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, any one of the above-mentioned methods for inverting deep well gas invasion formation parameters based on a gas-liquid two-phase flow model is implemented.

[0085] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any one of the above-mentioned methods for inverting deep well gas invasion formation parameters based on a gas-liquid two-phase flow model.

[0086] Compared with the prior art, the advantages of the present invention are:

[0087] The formation parameter inversion method provided by the present invention can accurately invert the formation parameters, provide a basis for accurate prediction and effective control of gas invasion, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 , schematic diagram of gas-liquid two-phase flow in gas-invasion wellbore;

[0089] Figure 2 , the wellbore-time system grid used to solve the flow equations;

[0090] Figure 3 , formation parameter inversion flow chart;

[0091] Figure 4 , the comparison chart between the inversion value and the true value of formation parameters;

[0092] Figure 5 , the curve diagram of the liquid level increment and bottom hole pressure change with time in the formation parameter inversion pool;

[0093] Figure 6 , comparison chart of the calculated and inverted values ​​of observed variables. DETAILED DESCRIPTION

[0094] The specific implementation mode of the present invention is described below in conjunction with embodiments:

[0095] It should be noted that the structures, proportions, sizes, etc. shown in this specification are only used to match the contents disclosed in the specification so that people familiar with this technology can understand and read them, and are not used to limit the conditions under which the present invention can be implemented. Any structural modification, change in proportional relationship or adjustment of size should still fall within the scope of the technical content disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.

[0096] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of description and are not used to limit the scope of implementation of the present invention. Changes or adjustments to their relative relationships should be regarded as the scope of implementation of the present invention without substantially changing the technical content.

[0097] Embodiment 1:

[0098] The present invention provides a deep well gas invasion formation parameter inversion method and system based on a gas-liquid two-phase flow model. First, based on the wellbore flow equation, a gas-liquid two-phase flow model is established (the wellbore flow equation (model) includes: annular space transient gas-liquid two-phase flow model, liquid phase single-phase flow control equation and auxiliary equation in the drill pipe), and the mathematical model is discretely solved by a finite difference algorithm; then, an unscented Kalman filter (UKF) is combined to construct an inversion model of formation parameters, and the formation pressure and production index in the gas invasion process are inverted using the measured data of the riser pressure and the liquid inlet and outlet flow difference. The formation parameter inversion method provided by the present invention can accurately invert the formation parameters, provide a basis for accurate prediction and effective control of gas invasion, and has broad application prospects.

[0099] The present invention provides a deep well gas invasion formation parameter inversion method, the main steps of which include:

[0100] 1. Establishment of wellbore flow model

[0101] First, in order to establish the annular transient gas-liquid two-phase flow model, the following assumptions are made:

[0102] (1) Ignore the distribution of flow velocity in the wellbore cross section and only consider the one-dimensional axial flow in the wellbore;

[0103] (2) The wellbore temperature selects a linear geothermal gradient;

[0104] (3) Ignore the effect of drilling cuttings on the annular air-liquid two-phase flow.

[0105] 1. Control equations of gas-liquid two-phase flow in annulus

[0106] The governing equations of annular air-liquid two-phase flow include three equations: the drilling fluid mass conservation equation, the intruding gas mass conservation equation, and the gas-liquid mixture momentum conservation equation.

[0107] The drilling fluid mass conservation equation is:

[0108]

[0109] Where: a is the drilling fluid density in the annulus, kg / m 3 ; α l is the drilling fluid volume fraction, dimensionless; v l is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of ​​the annulus, m 2 .

[0110] The mass conservation equation of the intruding gas is:

[0111]

[0112] Where: g is the gas density, kg / m 3 ; α g is the gas phase volume fraction, dimensionless; v g is the gas velocity, m / s.

[0113] The mixture momentum conservation equation is:

[0114]

[0115] Where: g is the acceleration due to gravity, 9.81m / s 2 ;P a is the annulus pressure, Pa; θ is the wellbore inclination, ° (starting from the vertical direction); F f is the friction pressure drop per unit length, Pa / m.

[0116] The sum of the drilling fluid volume fraction and the invading gas volume fraction is 1:

[0117] α g +α l =1 (4)

[0118] In the drift flow equation, the gas phase velocity can be expressed as:

[0119] v g =C0(v g α g +v l α l )+v gr (5)

[0120] Where: C0 is the slip coefficient; v gr is the slip velocity, m / s.

[0121] According to the equation proposed by Shi et al., the slip coefficient and slip velocity can be expressed as:

[0122]

[0123] Where: A is the gas phase distribution coefficient in the liquid; γ is the reduction term of the slip coefficient; v c is the characteristic velocity, m / s.

[0124] According to the PVT model, the density of gas can be expressed as:

[0125]

[0126] Where M g is the gas molar mass, kg / mol; R is the gas constant, J / mol / K; Z is the gas deviation factor, calculated using the following formula:

[0127]

[0128] In the formula, A1~A 11 is the coefficient; T r is the comparative temperature, dimensionless; ρ r is the comparative density, dimensionless.

[0129] 2. Control equation of single-phase flow of liquid in drill pipe

[0130] The governing equation of single-phase flow of liquid in the drill pipe includes two equations: the drilling fluid mass conservation equation and the drilling fluid momentum conservation equation.

[0131] The drilling fluid mass conservation equation is:

[0132]

[0133] Where: d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the cross-sectional area of ​​the drill pipe, m 2 .

[0134] The momentum conservation equation in the drill pipe is:

[0135]

[0136] Where: P d D is the drilling fluid pressure in the pipe, Pa; d is the inner diameter of the drill pipe, m.

[0137] 3. Auxiliary equations

[0138] The friction pressure drop per unit length F in the momentum conservation equation (Equation 3 and Equation 11) f The calculation formula is:

[0139]

[0140] Where: F f is the friction pressure drop per unit length, Pa / m; f is the Moody friction factor; D is the flow channel diameter (pipe inner diameter in drill pipe; hydraulic diameter in annulus), m; ρ is the density, kg / m 3 ; v is the fluid velocity, m / s.

[0141] The Moody friction factor f in formula (12) takes into account the influence of wall roughness and can be obtained by the following formula:

[0142]

[0143] Where Re is the Reynolds number;

[0144] In the gas-liquid two-phase flow model of gas invasion, equation (14) is used to define the relationship between the gas invasion rate, production index and formation pressure.

[0145] q g =J(P e -P b ) (14)

[0146] In the formula, q g is the gas invasion rate, kg / s; J is the production index, kg / s / MPa; P e is the formation pressure, MPa; P b is the bottom hole pressure, MPa, P b It can be calculated using the gas-liquid two-phase flow model.

[0147] 4. Model solution (finite difference method)

[0148] The entire wellbore is discretized into N nodes, such as Figure 2 The finite difference method is used to solve the flow control equations of the wellbore-formation system.

[0149] The annular flow equation (Formula 1-3) can be expressed as:

[0150]

[0151] Wherein, variables W, F(W) and Q(W) are functions of density, velocity, volume fraction and pressure; j = 1, 2 represent the mass conservation equations of liquid and gas phases; j = 3 represents the momentum conservation equation of gas-liquid two phases.

[0152] The mass conservation equation can be expressed as:

[0153]

[0154] 2. Formation parameter inversion method

[0155] During the gas invasion process, the surface inlet and outlet flow difference and the standpipe pressure can be measured. Therefore, the formation pressure and production index during the gas invasion process are inverted using the measured data of the inlet and outlet flow difference and the standpipe pressure.

[0156] If the gas reaches the wellhead after gas invasion, the invasion volume is very large and it is impossible to prevent the gas from reaching the wellhead on site without taking well control measures (1m 3 pool level increase).

[0157] The inlet and outlet flow difference of the ground at different times is the inlet and outlet flow difference of the liquid single-phase flow, which can be expressed as:

[0158] Δq(t)=[Δq(t1),Δq(t2),…,Δq(t N )] (17)

[0159] Δq(t)=q out (t)-q in (t) (18)

[0160] Where t is time, s; Δq is the flow difference between the inlet and outlet of the liquid, m 3 / min;q out is the liquid outlet flow difference, m 3 / min;q in is the liquid inlet flow difference, m 3 / min.

[0161] The riser pressure data measured at different times can be expressed as:

[0162] P sp (t) = [P sp (t1),P sp (t2),…,P sp (t N )] (19)

[0163] Where P sp is the standpipe pressure, MPa.

[0164] Taking formation pressure and production index as inversion parameters, the inversion parameters at different times are:

[0165] P e (t) = [P e (t1),P e (t2),…,P e (t N )] (20)

[0166] J(t)=[J(t1),J(t2),…,J(t N )] (twenty one)

[0167] Where P e is the formation pressure, MPa; J is the production index, kg / s / MPa.

[0168] Combined with the UKF algorithm, the formation pressure and production index are taken as state values, the inlet and outlet flow difference and the standpipe pressure are taken as observation values, and the state variable (X) and observation variable (Z) in the inversion model can be expressed as:

[0169] X(k)=[P e (k),J(k)] T (twenty two)

[0170] Z(k)=[Δq(k),P sp (k)] T (twenty three)

[0171] The state model f(·) for formation parameter inversion using the UKF algorithm can be expressed as:

[0172] X(k)=X(k-1)+W(k) (24)

[0173] The formation parameter inversion process is as follows: Figure 3 shown.

[0174] Embodiment 2:

[0175] The present invention is further described below in conjunction with a simulated well.

[0176] Based on the gas invasion wellbore inversion model established in the above-mentioned embodiment 1, combined with artificially generated data, the formation pressure and production index are interpreted and calculated in real time. First, the formation pressure and production index are preset as the true value of the inversion, and the standpipe pressure and the inlet and outlet flow difference are calculated using the gas-liquid two-phase flow model. On this basis, noise is added as the measurement data, and the inversion model is used for inversion. The basic data of the simulated well used in the present invention are shown in Table 1.

[0177] Table 1 Related parameters of simulated wells

[0178]

[0179] When the inverted formation parameters are two (i.e., the formation pressure and formation production index are inverted simultaneously), the three related parameters in the unscented Kalman filter are set to: α = 0.1, β = 2, κ = 1. The standard deviations of the system noise of the formation pressure and production index are set to 0.01 and 0.0002, respectively, and the standard deviations of the standpipe pressure and liquid inlet and outlet flow difference measurement noise are set to 0.02 and 0.0001, respectively. Therefore, the covariance matrix of the inversion model is Q = diag[0.01 2 ,0.0002 2 ], R=diag[0.02 2 ,0.0001 2 ]. The initial values ​​of the inversion of formation pressure and production index are set to 75MPa and 0.058kg / s / MPa, respectively.

[0180] Figure 4 The inversion results of formation pressure and formation production index under this condition are shown. Figure 4 a) and the lower part ( Figure 4b) Comparison of the inverted values ​​and true values ​​of formation pressure and production index. The pink background part (0-1640s) in the figure is the gas invasion period, and the gas migrates toward the wellhead but does not reach the wellhead; the yellow background part (after 1840s) is the gas overflowing the wellhead. It can be clearly seen from the figure that the formation parameters gradually approach the true value and remain stable after inversion. After 1000s, the relative error of formation pressure is controlled within 0.1%, while the relative error of production index is controlled within 8%. Therefore, it is not difficult to conclude that the formation parameter inversion has achieved good results before the gas overflows the wellhead.

[0181] Table 2 shows the error analysis results of formation pressure and production index. During the inversion process, the RMSE of formation pressure is 0.232, the ARE is 0.14%, and the e max The inversion result tends to be stable, that is, e after 1000s is 1.76%, which is the error between the inversion preset value and the true value of the formation pressure at the initial moment of gas invasion. ave The maximum relative error of the production index is 47.8% of the initial moment, its ARE is 16.2%, and the root mean square error RMSE is 0.015. ave It is 5.43%.

[0182] Table 2- Error analysis of formation parameter inversion results

[0183]

[0184] Figure 5 The curve of the change of pool liquid level increment and bottom hole pressure over time. It can be seen from the red line that it increases to the warning value of 1m at 2320s. 3 Above, the bottom hole pressure dropped to 74.05MPa. Before that, the model could accurately invert the formation pressure and production index.

[0185] Figure 6 (a) and Figure 6 (b) Comparison of the observed and inverted values ​​of the riser pressure and the liquid inlet and outlet flow rate difference. The observed values ​​are calculated by the gas-liquid two-phase flow model, while the inverted values ​​are obtained by the inversion model through UKF inversion. It can be seen that the inverted values ​​are basically consistent with the observed values, whether it is the riser pressure or the liquid inlet and outlet flow rate difference. This shows that the model can quickly and accurately predict unknown formation parameters and provide an accurate basis for subsequent wellbore pressure control.

[0186] In the inversion simulation of artificial synthetic data, there is a large deviation between the formation parameters and the true values ​​at the initial gas invasion moment. As the inversion calculation proceeds, the predicted values ​​of the state variables quickly approach their true values ​​and remain stable, indicating that the inversion model has high accuracy. In addition, since the formation pressure and production index have different contributions to the riser pressure and the liquid inlet and outlet flow difference, the inversion results of the two are also different. In this study, the inversion effect of formation pressure is better than that of production index.

[0187] From the above data, it can be seen that the present invention provides a deep well gas invasion formation parameter inversion method, which can quickly and accurately invert formation parameters, and the inversion model achieves a high inversion accuracy before the pool liquid level increases to the warning value and the gas overflows the wellbore. At the same time, the inversion value of the riser pressure and the liquid inlet and outlet flow difference is highly consistent with the observed value, that is, the result calculated by the wellbore flow model, which also shows that the inversion of formation pressure and production index is more accurate and reliable.

[0188] Embodiment 3:

[0189] The present invention provides a deep well gas invasion formation parameter inversion system based on a gas-liquid two-phase flow model, which can be used to implement the above-mentioned deep well gas invasion formation parameter inversion method based on a gas-liquid two-phase flow model. Specifically, the deep well gas invasion formation parameter inversion system based on a gas-liquid two-phase flow model comprises:

[0190] Wellbore flow modeling module, used to establish wellbore flow model;

[0191] A finite difference discretization module is used for discretizing and solving the wellbore flow model based on the established wellbore flow model by using a finite difference algorithm;

[0192] Unscented Kalman filter inversion module, used to build an inversion model of formation parameters in combination with unscented Kalman filter UKF;

[0193] The data fusion and inversion module is used to invert the formation pressure and production index during the gas invasion process using the measured data of the riser pressure and the liquid inlet and outlet flow difference.

[0194] Embodiment 4:

[0195] This embodiment provides a terminal device, which includes a processor and a memory, wherein the memory is used to store a computer program, wherein the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of a deep well gas invasion formation parameter inversion method based on a gas-liquid two-phase flow model, including the following steps:

[0196] A wellbore flow model is established, and the model is discretely solved using the finite difference algorithm. An inversion model of formation parameters is constructed by combining the unscented Kalman filter (UKF), and the formation pressure and production index during gas invasion are inverted using the measured data of riser pressure and liquid inlet and outlet flow rate difference.

[0197] Embodiment 5:

[0198] This embodiment provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It is understandable that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory.

[0199] The processor may load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the deep well gas invasion formation parameter inversion method based on the gas-liquid two-phase flow model in the above embodiment; the processor may load and execute the following steps of one or more instructions in the computer-readable storage medium:

[0200] A wellbore flow model is established, and the model is discretely solved using the finite difference algorithm. An inversion model of formation parameters is constructed by combining the unscented Kalman filter (UKF), and the formation pressure and production index during gas invasion are inverted using the measured data of riser pressure and liquid inlet and outlet flow rate difference.

[0201] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0202] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0203] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0204] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0205] The preferred embodiments of the present invention are described in detail above, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

[0206] Many other changes and modifications may be made without departing from the concept and scope of the present invention.It should be understood that the present invention is not limited to the specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A deep well gas invasion formation parameter inversion method based on a gas-liquid two-phase flow model, characterized in that: The method comprises: A wellbore flow model is established, and the model is discretely solved using the finite difference algorithm. An inversion model of formation parameters is constructed by combining the unscented Kalman filter (UKF), and the formation pressure and production index during gas invasion are inverted using the measured data of riser pressure and liquid inlet and outlet flow rate difference.

2. The method for inversion of deep well gas invasion formation parameters based on a gas-liquid two-phase flow model according to claim 1, characterized in that: Establish a wellbore flow model, including: The first step is to build a gas-liquid two-phase flow control model in the annulus: First, the model ignores the cross-sectional velocity distribution, the temperature gradient is linear, and the influence of drilling cuttings is not considered. Then the following equations are established: the drilling fluid mass conservation equation, the intruding gas mass conservation equation, and the gas-liquid mixture momentum conservation equation; The drilling fluid mass conservation equation is: Where: a is the drilling fluid density in the annulus, kg / m 3 ; α l is the drilling fluid volume fraction, dimensionless; v l is the drilling fluid velocity in the annulus, m / s; A a is the cross-sectional area of ​​the annulus, m 2 ; The mass conservation equation of the intruding gas is: Where: g is the gas density, kg / m 3 ; α g is the gas phase volume fraction, dimensionless; v g is the gas velocity, m / s; The mixture momentum conservation equation is: Where: g is the acceleration due to gravity, 9.81m / s 2 ;P a is the annulus pressure, Pa; θ is the wellbore inclination, ° (starting from the vertical direction); F f is the friction pressure drop per unit length, Pa / m; The sum of the drilling fluid volume fraction and the invading gas volume fraction is 1: α g +α l ＝1 (4) In the drift flow equation, the gas phase velocity can be expressed as: v g =C0(v g α g +v l α l )+v gr (5) Where: C0 is the slip coefficient; v gr is the slip velocity, m / s; The slip coefficient and slip velocity can be expressed as: Where: A is the gas phase distribution coefficient in the liquid; γ is the reduction term of the slip coefficient; v c is the characteristic speed, m / s; According to the PVT model, the density of gas can be expressed as: Where M g is the gas molar mass, kg / mol; R is the gas constant, J / mol / K; Z is the gas deviation factor, calculated using the following formula: In the formula, A1~A 11 is the coefficient; T r is the comparative temperature, dimensionless; ρ r For comparison density, dimensionless; The second step is to construct the control equation of the single-phase flow of liquid in the drill pipe: The governing equations of the single-phase flow of liquid in the drill pipe include two equations: the drilling fluid mass conservation equation and the drilling fluid momentum conservation equation; The drilling fluid mass conservation equation is: Where: d is the density of drilling fluid in the drill pipe, kg / m 3 ;v d is the drilling fluid velocity in the drill pipe, m / s; A d is the cross-sectional area of ​​the drill pipe, m 2 ; The momentum conservation equation in the drill pipe is: Where: P d D is the drilling fluid pressure in the pipe, Pa; d is the inner diameter of the drill pipe, m; The third step is to construct the auxiliary equation: The momentum conservation equation, i.e. the friction pressure drop per unit length F in Equation 3 and Equation 11 f The calculation formula is: Where: F f is the friction pressure drop per unit length, Pa / m; f is the Moody friction factor; D is the flow channel diameter, the inner diameter of the pipe in the drill pipe; the hydraulic diameter in the annulus, m; ρ is the density, kg / m 3 ; v is the fluid velocity, m / s; The Moody friction factor f in formula (12) takes into account the influence of wall roughness and can be obtained by the following formula: Where Re is the Reynolds number; In the gas-liquid two-phase flow model of gas invasion, equation (14) is used to define the relationship between the gas invasion rate, production index and formation pressure; q g =J(P e -P b ) (14) In the formula, q g is the gas invasion rate, kg / s; J is the production index, kg / s / MPa; P e is the formation pressure, MPa; P b is the bottom hole pressure, MPa, P b It can be calculated using the gas-liquid two-phase flow model.

3. The method for inversion of deep well gas invasion formation parameters based on a gas-liquid two-phase flow model according to claim 1, characterized in that: The discrete solution of the model using the finite difference algorithm specifically includes: The entire wellbore is discretized into N nodes, and the flow control equations of the wellbore-formation system are solved using the finite difference method; The annular flow equation is expressed as: Wherein, variables W, F(W) and Q(W) are functions of density, velocity, volume fraction and pressure; j = 1, 2 represent the mass conservation equations of liquid and gas phases; j = 3 represents the momentum conservation equation of gas-liquid two phases; The mass conservation equation is expressed as:

4. The method for inversion of deep well gas invasion formation parameters based on a gas-liquid two-phase flow model according to claim 1, characterized in that: During the gas invasion process, the difference in ground inlet and outlet flow and the riser pressure can be measured; the formation pressure and production index during the gas invasion process are inverted using the measured data of the difference in inlet and outlet flow and the riser pressure; The inlet and outlet flow difference of the ground at different times is the inlet and outlet flow difference of the liquid single-phase flow, which is expressed as: Δq(t)=[Δq(t1),Δq(t2),…,Δq(t N )] (17) Δq(t)=q out (t)-q in (t) (18) Where t is time, s; Δq is the flow difference between the inlet and outlet of the liquid, m 3 / min;q out is the liquid outlet flow difference, m 3 / min;q in is the liquid inlet flow difference, m 3 / min; The riser pressure data measured at different times are expressed as: P sp (t)=[P sp (t1),P sp (t2),…,P sp (t N )] (19) Where P sp is the standpipe pressure, MPa; Taking formation pressure and production index as inversion parameters, the inversion parameters at different times are: P e (t)=[P e (t1),P e (t2),…,P e (t N )] (20) J(t)=[J(t1),J(t2),…,J(t N )] (21) Where P e is the formation pressure, MPa; J is the production index, kg / s / MPa; Combined with the UKF algorithm, the formation pressure and production index are taken as state values, the inlet and outlet flow difference and the standpipe pressure are taken as observation values, and the state variable (X) and observation variable (Z) in the inversion model are expressed as follows: X(k)=[P e (k),J(k)] T (22) Z(k)=[Δq(k),P sp (k)] T (23) The state model f(·) for formation parameter inversion using UKF algorithm is expressed as: X(k)=X(k-1)+W(k) (24).

5. A deep well gas invasion formation parameter inversion system based on a gas-liquid two-phase flow model, characterized in that: The system comprises: Wellbore flow modeling module, used to establish wellbore flow model; A finite difference discretization module is used for discretizing and solving the wellbore flow model based on the established wellbore flow model by using a finite difference algorithm; Unscented Kalman filter inversion module, used to build an inversion model of formation parameters in combination with unscented Kalman filter UKF; The data fusion and inversion module is used to invert the formation pressure and production index during the gas invasion process using the measured data of the riser pressure and the liquid inlet and outlet flow difference.

6. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, a method for inversion of deep well gas invasion formation parameters based on a gas-liquid two-phase flow model as described in any one of claims 1 to 4 is implemented.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, implements a deep well gas invasion formation parameter inversion method based on a gas-liquid two-phase flow model according to any one of claims 1 to 4.

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