A method for constructing a model to dynamically calculate well connectivity parameters

Abstract

The present invention discloses a method for constructing a model to dynamically calculate well-to-well connectivity parameters, including sequentially establishing a balance equation, a flow equation and a momentum equation and deriving a static capacitance model; defining the state variables of the static capacitance model and fusing them to construct a state variable model; performing an extended Kalman filter on the state variable model to establish a dynamic capacitance model; using the injection volume and liquid production volume data with the same time period as input parameters, and using the dynamic capacitance model to calculate and obtain the parameters of the state variables that dynamically change according to the corresponding time step. The present invention defines its state variables after constructing a static capacitance model, and fuses the state variables with the static capacitance model to construct a state variable model, and then performs an extended Kalman filter on the state variable model to establish a dynamic capacitance model, so as to obtain the parameters of the state variables that dynamically change according to the time step after inputting the injection volume and liquid production volume data with the same time period.

Description

Technical Field

[0001] The invention relates to the technical field of oil reservoir management, and in particular to a method for constructing a model to dynamically calculate well-to-well connectivity parameters. Background Art

[0002] Well connectivity refers to the ability of fluid transfer and communication between different wells in an oil reservoir. Accurately evaluating well connectivity helps to understand the dynamic behavior of fluids inside the reservoir to maximize the recovery rate and economic benefits of the oil field. Conventional methods for characterizing well connectivity can be divided into two categories: static data system analysis methods and dynamic data system analysis methods. Among them, dynamic data system analysis methods can more accurately reflect the actual production status and dynamic changes of the reservoir and are widely used.

[0003] At present, the commonly used dynamic data system analysis methods are mainly capacitance model method or Kalman filter method. The capacitance model method is a dynamic analysis method derived from the inversion of well connectivity from injection and production data. It reveals the essential characteristics of the injection and production system based on the principle of material balance. However, the connectivity parameters and time lag coefficients in the capacitance model are usually regarded as fixed values. This static processing method may not accurately reflect the true dynamics of the oil field evolution over time, especially when capturing continuous changes caused by oil production activities. The Kalman filter method uses the prediction of observed data and models to optimize the estimation results, and quantifies the uncertainty of the estimation through the covariance matrix. It can effectively handle the uncertainty and noise in the data, and takes into account the time change and dynamic characteristics. However, the Kalman filter method relies on continuous and stable production data, and for irregular production conditions, such as well shutdown, it often cannot provide accurate predictions, which limits its universal applicability under complex field conditions.

[0004] Therefore, the existing method of calculating the well connectivity parameters by using a single capacitance model method or a Kalman filter method is difficult to accurately reflect the real dynamics of the oil field evolution over time to provide accurate predictions. Summary of the invention

[0005] The purpose of the present invention is to provide a method for constructing a model to dynamically calculate well-to-well connectivity parameters, so as to solve the technical problem that a single dynamic data system analysis method in the prior art is difficult to accurately reflect the real dynamics of the oil field evolving over time to provide accurate predictions.

[0006] In order to solve the above technical problems, the present invention specifically provides the following technical solutions:

[0007] A method for constructing a model to dynamically calculate well connectivity parameters comprises the following steps:

[0008] Step 100: establishing a material balance equation, a flow equation and a momentum equation describing the connectivity between the wells in sequence according to the production data of the injection wells and the production wells, and deriving a static capacitance model characterizing the connectivity between the injection wells and the production wells according to the balance equation, the flow equation and the momentum equation;

[0009] Step 200: define state variables based on the static capacitance model, and fuse the state variables with the static capacitance model to construct a state variable model of the static capacitance model;

[0010] Step 300: Based on the state variable model of the static capacitance model, the state variable model is subjected to extended Kalman filtering by using an extended Kalman filtering method to establish a dynamic capacitance model;

[0011] Step 400: using the injection volume and liquid production volume data with the same time period as input parameters, and using the dynamic capacitance model to calculate and obtain the parameters of the state variables that dynamically change according to the corresponding time step.

[0012] As a preferred solution of the present invention, the state variable includes three state variable parameters, namely, an initial imbalance constant, a connectivity coefficient from the injection well to the production well, and a time lag coefficient.

[0013] As a preferred solution of the present invention, in step 100, the specific method of deriving and obtaining the static capacitance model is:

[0014] Based on the principle that the total mass of the material between wells is constant, the equilibrium equation is established:

[0015]

[0016] Among them, C t is the compression coefficient; V ij is the pore volume; is the time rate of change of the average pressure; Q wi (t) is the injection volume of injection well i at time t; Q ij (t) is the flow rate of production well j at time t; λ ij is the connectivity coefficient;

[0017] Given the production index of a production well, the flow equation is established:

[0018]

[0019] Among them, J j is the productivity index of production well j; is the average pressure between injection well i and production well j; P wfj is the bottom hole flowing pressure of production well j;

[0020] Based on the balance equation and flow equation, the momentum equation is established:

[0021]

[0022] in, is the rate of change of flow rate of production well j over time; is the rate of change of bottom hole pressure with time; τ ij is the time lag coefficient;

[0023] Since the bottom hole pressure fluctuation of the production well is much smaller than the liquid production, the simplified momentum equation is:

[0024]

[0025] Using the superposition principle and momentum simplified equation, the equation for calculating the total liquid production is:

[0026]

[0027] Among them, Q j (t) is the total liquid production of the production well; Q wi (ζ) is the injection volume of injection well i at time ζ;

[0028] Discretize the total liquid production equation by time step to obtain the static capacitance model:

[0029]

[0030] Among them, Q j (n) is the total liquid production of the jth production well at the nth time step; β j is the initial constant of imbalance; Q wi (m) is the injection volume of the ith injection well at the mth time step, and m=n-1.

[0031] As a preferred solution of the present invention, in step 200, the specific method of fusing the state variable with the static capacitance model to construct the state variable model is:

[0032] Based on the static capacitance model, three state variables β are defined: j , ij , τ ij , these three state variables are described by the state vector to obtain the state vector equation:

[0033] x i (m)=[x(m),x1(m),x2(m)]'

[0034] =[β j (m),λ ij (m),τ ij (m)]';

[0035] Among them, x i (m) is a 3×1 state vector matrix; x(m) represents β j (m); x1(m) represents λ ij (m); x2(m) represents τ ij (m);

[0036] Based on the state vector equation, the standard solution method proposed by Mendel is used to obtain the multi-injection and multi-collection state variable model:

[0037]

[0038] Among them, P i c (n) represents Q j (n) is the total liquid production in the current time step; n xi (m) represents the system state noise.

[0039] As a preferred solution of the present invention, in step 300, the specific method of performing extended Kalman filtering on the state variable model to establish a dynamic capacitance model is:

[0040] Based on the mathematical model of the system state changing with time, the a priori estimation equation of the extended Kalman filter under discrete time is established:

[0041] X(k|k-1)=FX(k-1|k-1)+n x (k-1);

[0042] Among them, X(k|k-1) represents x(n) at time k, which is the state of the system at time k; X(k-1|k-1) represents x(m) at time k, which is the optimal estimate of the state of the system at time k-1; F is the state matrix; n x (k-1) is the process noise;

[0043] Based on the prior estimation equation, the error covariance prediction equation describing the uncertainty range of the system is established:

[0044] P(k|k-1)=FP(k-1|k-1)F T +Q;

[0045] Among them, P(k|k-1) is the optimal estimation error covariance at the previous moment; F T is the transposed matrix of F; Q is the process noise n x (k-1) covariance matrix;

[0046] Based on the system state and its related state quantities, a measurement equation is established to describe the relationship between the system state and the observed value:

[0047] Z(k)=HX(k)+V(k);

[0048] Where Z(k) represents Q j (n) and P(n) are the actual measured values ​​at time k; V(k) is the measurement noise; n is the current time k; m is the previous time k-1; H is the observation matrix;

[0049] Based on the observed and predicted values, a measurement residual equation is established to describe the difference between the observed and predicted values:

[0050] y(k)=Z(k)-HX(k|k-1);

[0051] Among them, Z(k) is the actual measurement value; HX(k|k-1) is the predicted measurement value;

[0052] The Kalman gain equation is obtained based on the measurement residual equation:

[0053]

[0054] Based on the measurement residual equation and the Kalman gain equation, the optimal estimation equation is established:

[0055] X(k|k)=X(k|k-1)+K g (k)[Z(k)-HX(k|k-1)];

[0056] Among them, X(k|k) is the optimal state estimate at time k; X(k|k-1) is the state prediction at time k;

[0057] Update the error covariance of the optimal estimation equation to obtain the optimal error covariance equation:

[0058] P(k|k)=[1-K g (k)H]P(k|k-1);

[0059] Among them, the observation matrix H contains state variable parameters, the prior estimation equation and the error covariance prediction equation, which are cyclically updated with time steps through the optimal estimation equation and the optimal error covariance equation to obtain the observation matrix H of the corresponding time step, that is, the state variable parameters of the corresponding time step.

[0060] As a preferred solution of the present invention, the state matrix F is a 3N×3N Jacobian matrix, specifically:

[0061]

[0062] Among them, F x Determined by the number of wellheads, and defined as A i is the diagonal matrix of a single well.

[0063] As a preferred solution of the present invention, in step 400, the specific method of using the dynamic capacitance model to calculate and obtain the parameters of the state variables of the corresponding time step is:

[0064] Let the static capacitance model be h, then:

[0065]

[0066] Then the calculation is:

[0067]

[0068] Based on the dynamic capacitance model, the observation matrix H of the corresponding time step is obtained, and the injection amount Q with the same time period is wi (m) and liquid production Q j (n) The data is brought into each of the observation matrices H to obtain the connectivity coefficient λ that changes dynamically according to the corresponding time step ij and the time lag coefficient τ ij .

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] The present invention defines its state variables after constructing a static capacitance model, and fuses the state variables with the static capacitance model to construct a state variable model. The state variable model is then expanded by Kalman filtering to establish a dynamic capacitance model, so as to obtain the parameters of the state variables that dynamically change according to the time step after inputting the injection volume and liquid production volume data with the same time period. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0072] Figure 1 A schematic diagram of a flow chart of a method for dynamically calculating well-to-well connectivity parameters by constructing a model provided in an embodiment of the present invention;

[0073] Figure 2 A schematic diagram of a reservoir model for the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention;

[0074] Figure 3 A parameter chart of the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention;

[0075] Figure 4 A water analysis diagram of the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention;

[0076] Figure 5 A water analysis diagram of the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention;

[0077] Figure 6 A comparative analysis diagram of connectivity coefficients during the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention;

[0078] Figure 7 A comparative analysis diagram of the time lag coefficients during the verification process of the method for dynamically calculating well-to-well connectivity parameters by constructing a model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0079] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] like Figure 1 As shown, the present invention provides a method for constructing a model to dynamically calculate well-to-well connectivity parameters, comprising the following steps:

[0081] Step 100: establishing a material balance equation, a flow equation and a momentum equation describing the connectivity between the wells in sequence according to the production data of the injection wells and the production wells, and deriving a static capacitance model characterizing the connectivity between the injection wells and the production wells according to the balance equation, the flow equation and the momentum equation;

[0082] Step 200: define state variables based on the static capacitance model, and fuse the state variables with the static capacitance model to construct a state variable model of the static capacitance model;

[0083] Step 300: Based on the state variable model of the static capacitance model, the state variable model is subjected to extended Kalman filtering by using an extended Kalman filtering method to establish a dynamic capacitance model;

[0084] Step 400: using the injection volume and liquid production volume data with the same time period as input parameters, and using the dynamic capacitance model to calculate and obtain the parameters of the state variables that dynamically change according to the corresponding time step.

[0085] The method for calculating the well-to-well connectivity parameters in this embodiment is mainly based on defining the state variables of the static capacitance model, constructing a state variable model, and using the extended Kalman filtering method to extend the Kalman filtering of the state variable model to obtain a dynamic capacitance model. The dynamic capacitance model includes state variables that change dynamically according to the time step. After the injection volume and liquid production data with the same time period are input into the dynamic capacitance model, the state variables of the corresponding time step are calculated.

[0086] The state variables include three state variable parameters, namely, the initial imbalance constant β j , the connectivity parameter λ from the injection well to the production well ij and the time lag coefficient τ ij .

[0087] The connectivity parameter λ that changes dynamically according to the time step is obtained by calculation ij and the time lag coefficient τ ij , which can effectively and dynamically describe the connectivity between wells and help calculate and continuously update the connectivity parameter λ ij and the time lag coefficient τ ij , thereby reflecting reservoir dynamics more accurately and timely.

[0088] Compared with the existing single-state data system analysis method, the method for calculating the well connectivity parameters in this embodiment can define the initial constant β containing the imbalance after constructing the static capacitance model. j , connectivity parameter λ ij , time lag coefficient τ ij The state variable model is constructed by the state variable, and the extended Kalman filter method is used to continuously update and obtain the connectivity parameter λ that changes dynamically according to the time step ij and the time lag coefficient τ ij , thereby reflecting reservoir dynamics more accurately and timely.

[0089] In step 100, the specific method of deriving the static capacitance model is:

[0090] Assuming that an oil reservoir contains several injection wells and production wells, the equilibrium equation is established based on the principle that the total mass of the material between the wells is constant:

[0091]

[0092] Among them, C t is the compression coefficient; V ij is the pore volume; is the time rate of change of the average pressure; Q wi (t) is the injection volume of injection well i at time t; Q ij (t) is the flow rate of production well j at time t; λ ijis the connectivity coefficient;

[0093] Given the production index of a production well, the flow equation is established:

[0094]

[0095] Among them, J j is the productivity index of production well j; is the average pressure between injection well i and production well j; P wfj is the bottom hole flowing pressure of production well j;

[0096] Based on the balance equation and flow equation, the momentum equation is established:

[0097]

[0098] in, is the rate of change of flow rate of production well j over time; is the rate of change of bottom hole pressure with time; τ ij is the time lag coefficient;

[0099] Since the bottom hole pressure fluctuation of the production well is much smaller than the liquid production, the simplified momentum equation is:

[0100]

[0101] Using the superposition principle and momentum simplified equation, the equation for calculating the total liquid production is:

[0102]

[0103] Among them, Q j (t) is the total liquid production of the production well; Q wi (ζ) is the injection volume of injection well i at time ζ;

[0104] Discretize the total liquid production equation by time step to obtain the static capacitance model:

[0105]

[0106] Among them, Q j (n) is the total liquid production of the jth production well at the nth time step; β j is the initial constant of imbalance; Q wi (m) is the injection volume of the ith injection well at the mth time step, and m=n-1.

[0107] In this step, the initial imbalance constant β j It is considered to be included in the total liquid production Q j (n), based on this, the total liquid production Q is input into the static capacitance model j(n) and injection volume Q wi (m), the connectivity parameter λ can be obtained ij and the time lag coefficient τ ij .

[0108] The static capacitance model can only obtain the connectivity parameter λ at the current moment. ij and the time lag coefficient τ ij , the connectivity parameter λ cannot be known ij and the time lag coefficient τ ij The changes in the well connectivity during the production process make it impossible to understand the well connectivity. This is the deficiency of the existing model in describing the well connectivity.

[0109] In order to solve this problem, it is necessary to process the static capacitance model again through step 200. In step 200, the specific method of fusing the state variable with the static capacitance model to construct the state variable model is as follows:

[0110] Based on the static capacitance model, three state variables β are defined: j , ij , τ ij , these three state variables are described by the state vector to obtain the state vector equation:

[0111] x i (m)=[x(m),x1(m),x2(m)]'

[0112] =[β j (m),λ ij (m),τ ij (m)]';

[0113] Among them, x i (m) is a 3×1 state vector matrix; x(m) represents β j (m); x1(m) represents λ ij (m); x2(m) represents τ ij (m).

[0114] In this step, the unbalanced initial constant β in the static capacitance model is extracted j , connectivity parameter λ ij , time lag coefficient τ ij , which is used to establish a state vector matrix to independently describe the state variables in the static capacitance model.

[0115] Based on the state vector equation, the standard solution method proposed by Mendel is used to obtain the multi-injection and multi-collection state variable model:

[0116]

[0117] Among them, P ic (n) represents Q j (n) is the total liquid production in the current time step; n xi (m) represents the system state noise.

[0118] In this step, the state vector matrix is ​​fused with the static capacitance model to obtain a model describing the relationship between the state variables and the injection volume and the liquid production volume, namely, the state variable model.

[0119] In step 300, the specific method of performing extended Kalman filtering on the state variable model to establish a dynamic capacitance model is:

[0120] Based on the mathematical model of the system state changing with time, the a priori estimation equation of the extended Kalman filter under discrete time is established:

[0121] X(k|k-1)=FX(k-1|k-1)+n x (k-1);

[0122] Among them, X(k|k-1) represents x(n) at time k, which is the state of the system at time k; X(k-1|k-1) represents x(m) at time k, which is the optimal estimate of the state of the system at time k-1; F is the state matrix; n x (k-1) is the process noise.

[0123] In this step, the state matrix F is a 3N×3N Jacobian matrix, specifically:

[0124]

[0125] Among them, F x Determined by the number of wellheads, and defined as A i is the diagonal matrix of a single well. That is, A in the state matrix F i According to the definition of the number of wellheads, such as three wells A1, A2, and A3, the state variables between all injection wells and production wells can be described.

[0126] Based on the prior estimation equation, the error covariance prediction equation describing the uncertainty range of the system is established:

[0127] P(k|k-1)=FP(k-1|k-1)F T +Q;

[0128] Among them, P(k|k-1) is the optimal estimation error covariance at the previous moment; F T is the transposed matrix of F; Q is the process noise n x (k-1) covariance matrix.

[0129] In this step, the Kalman filter not only considers the estimation of the system, but also the uncertainty range of the estimated state. This "uncertainty range" is represented by the error covariance.

[0130] Based on the system state and its related state quantities, a measurement equation is established to describe the relationship between the system state and the observed value:

[0131] Z(k)=HX(k)+V(k);

[0132] Where Z(k) represents Q j (n) and P(n) are the actual measured values ​​at time k; V(k) is the measurement noise; n is the current time k; m is the previous time k-1; H is the observation matrix.

[0133] In this step, let the static capacitance model be h, then:

[0134]

[0135] Then the calculation is:

[0136]

[0137] The injection amount Q at time k wi (m) and liquid production Q j (n) The data is brought into the observation matrix H to obtain the connectivity coefficient λ at time k ij and the time lag coefficient τ ij .

[0138] The system state X(k) at time k is obtained from the system state at the previous time k-1 through the prior estimation equation, as follows:

[0139] Based on the observed and predicted values, a measurement residual equation is established to describe the difference between the observed and predicted values:

[0140] y(k)=Z(k)-HX(k|k-1);

[0141] Among them, Z(k) is the actual measurement value; HX(k|k-1) is the predicted measurement value;

[0142] The Kalman gain equation is obtained based on the measurement residual equation:

[0143]

[0144] Based on the measurement residual equation and the Kalman gain equation, the optimal estimation equation is established:

[0145] X(k|k)=X(k|k-1)+K g (k)[Z(k)-HX(k|k-1)];

[0146] Among them, X(k|k) is the optimal state estimate at time k; X(k|k-1) is the state prediction at time k.

[0147] In this step, the core idea of ​​the Kalman filter is to combine the model's prediction and the actual measurement to obtain an optimal state estimate. This "optimal" means minimizing the mean square value of the estimation error. Therefore, it is necessary to find a gain that minimizes the mean square value of the estimation error. Based on this, consider the variance of the measurement residual:

[0148] Var(y(k))=HP(k|k-1)H T +R;

[0149] Where R is the covariance of the measurement noise, and a K is required g (k) makes Var(y(k)) minimum, then the Kalman gain equation can be derived.

[0150] The optimal estimate is a combination of the predicted state and the correction based on the measurement. This correction is based on the difference between the predicted state and the actual measurement (i.e., the residual), and the optimal estimate equation can be obtained. Among them, the Kalman gain determines the degree of correction of the predicted state based on the measurement residual.

[0151] Finally, the estimated uncertainty or error covariance needs to be updated, which ensures that the system estimate is not only optimal but also consistent with the actual uncertainty.

[0152] Update the error covariance of the optimal estimation equation to obtain the optimal error covariance equation:

[0153] P(k|k)=[1-K g (k)H]P(k|k-1);

[0154] Among them, the observation matrix H contains state variable parameters, the prior estimation equation and the error covariance prediction equation, which are cyclically updated with time steps through the optimal estimation equation and the optimal error covariance equation to obtain the observation matrix H of the corresponding time step, that is, the state variable parameters of the corresponding time step.

[0155] Based on the above process, based on the state variable model and the static capacitance model, the observation matrix H of the corresponding time step is obtained by extending the Kalman filter, and the injection amount Q with the same time period is wi (m) and liquid production Q j (n) The data is brought into each of the observation matrices H to obtain the connectivity coefficient λ of the corresponding time step ij and the time lag coefficient τ ij .

[0156] In order to verify the accuracy and stability of the method for calculating the inter-well connectivity parameters of this embodiment, the following actual application performances of the Kalman filter method (SV) based solely on the state variable (Statevariable), the separate capacitance model method (TC) and the constructed dynamic capacitance model (SV-DC) are presented.

[0157] Verification of the accuracy of the SV-DC model:

[0158] First, the corresponding numerical model is established, and the production data (such as injection volume, liquid production, and production pressure difference) obtained from the numerical model are used as the input data of the model.

[0159] 1. Construction of numerical model:

[0160] For the three models mentioned above, the application in actual reservoirs includes calculating the well connectivity coefficient and other relevant physical parameters. This process requires dynamic data of injection volume and liquid production. These data must be complete time series with uniform time intervals. This verification method chooses the widely used reservoir simulator tNavigator to simulate oil field production. This choice is to ensure that comprehensive and consistent time series data are obtained.

[0161] In this model, the bottom hole pressure of the production well is always maintained at 600 bar. Initially, the bottom hole pressure of the injection well is 750 bar, and then adjusted to 800 bar, 900 bar and 850 bar at different stages. These adjustments are made with different rectangular pulse signals. The adjustment time is January 2024, January 2027 and January 2031, and each adjustment lasts for 6 months. A 3D reservoir model of 315m×315m×5m (length×width×height) was established, as shown in Figure 2. Figure 2 As shown. Figure 3 The table shown lists the rock physical parameters obtained from laboratory tests selected for the model.

[0162] 2. Analysis of water breakthrough time results:

[0163] like Figure 4 and Figure 5 , comprehensively showing the water breakthrough situation of the production wells. Figure 4 The figure shows the decreasing trend of oil saturation in the four production wells when water is generated. Figure 5 The corresponding water content curves of the production wells are shown. It is worth noting that the water breakthrough events of these production wells occurred on 2022.01.01, 2022.02.01, 2022.03.01 and 2022.07.01, indicating the formation of a continuous water circulation channel in the reservoir. This promotes the effective flow of water to the oil wells along the diagonal of the model, such as Figure 4As shown, water cones appear first in producer 4, followed by producers 3, 2, and 1. The relative permeabilities between these producers and water injectors vary, with producer 4 having the highest permeability. This has a greater impact on the water breakthrough process, which can be seen from the order of the producers.

[0164] 3. Comparison of inter-well connectivity and time lag coefficients of different methods:

[0165] First of all, it should be noted that the SV model can only obtain the dynamic well-to-well connectivity coefficient. On the other hand, the TC model and the SV-DC model can determine not only the well-to-well connectivity coefficient but also the time lag coefficient. The time lag coefficient is a physical quantity that represents the delay time for fluid to flow from one well to another. Comparative studies on the well-to-well connectivity coefficient using the SV model and the combined TC and SV-DC models are rare and have not been explored in a unified framework. Although these coefficients are intended to describe oil well connectivity, there are fundamental differences in physical concepts, basic assumptions, and the range of data used. This validation section conducts a comparative analysis of these coefficients to clarify how each method explains the connectivity between oil wells.

[0166] Figure 6 The well connectivity coefficients calculated by three models are shown: the results of the SV-DC model and the SV model are presented as solid lines and dashed lines, respectively, reflecting that the two models can capture the time variation characteristics of the well connectivity coefficients. The results of the TC model are represented by solid points because the model only provides static well connectivity coefficient estimates. In the gentle section, 2030-01-01, the relative errors of the dashed and solid lines are 19.5% (400mD), 18.5% (200mD), 15.7% (100mD), and 9% (30mD). The overall trends of the two are very close, especially after the first peak. In the fluctuating section, 2027-02-01, the relative errors of the three models range from 9% to 19.5%.

[0167] In the three pressure pulse stages (2024.01-2024.06, 2027.01-2027.06, 2031.01-2031.06), the well connectivity coefficients predicted by the SV-DC model and the SV model both showed a fluctuation behavior of increasing values, and the fluctuation range and fluctuation form of the two were very similar, which further confirmed the accuracy of the SV-DC model in accurately simulating the dynamic behavior of the reservoir. In addition, it can be observed that the SV-DC model has a more obvious pulse response effect on the pressure section (in the pressure pulse stage, the well connectivity coefficient curve of the SV-DC model shows a process of sudden rise-sudden drop-smooth-reduction). Of course, it can be observed that in the early stage of 2022-01-01, the curve change rules of the SV-DC and SV models are very different (SV-DC is a downward trend, SV is an upward trend). There are two main reasons for this difference. On the one hand, the mathematical structure of the model is different: the SV model is a differential equation, focusing on the recursive relationship at discrete time points, and describing a dynamic system model of single-step change. The SV-DC model is an integral effect model, which is a continuous superposition and summation relationship. It superimposes the effects of multiple inputs to predict an output. On the other hand, both models have undergone the extended Kalman filter (EKF) process. As an adaptive signal processing technology, the optimization algorithm of EKF will become more and more accurate over time, so there may be some degree of data fluctuation in the early stages of the model. This fluctuation reflects the self-regulation characteristics of the model. As more data is accumulated, the prediction results tend to be more accurate.

[0168] It is also observed that the trend of the interwell connectivity coefficient curves shown by the SV-DC model and the SV model is closely related to the permeability of the high-permeability channel. This trend clearly shows that as the permeability increases, the interwell connectivity coefficient increases accordingly, which is consistent with the understanding of reservoir characteristics. In short, the interwell connectivity coefficient of high permeability channels (such as 400mD) is significantly higher than that of low permeability channels (such as 30mD), which verifies the traditional understanding of reservoir fluid flow characteristics.

[0169] The SV-DC model is used to analyze the dynamic change of the time lag coefficient τ over time, which mainly reflects the fluid transmission time from the injection well to the production well. Figure 7 As shown in the figure, according to the model calculation results, it can be observed that the relationship between the τ values ​​of the four production wells is that, among the four production wells, the well with higher permeability has a smaller τ value. This means that in the rock formation with higher permeability, the fluid moves faster, so the fluid reaches the production well more quickly. This phenomenon is consistent with the "water breakthrough time result analysis" in the Figure 4 and Figure 5The water breakthrough time of the production wells observed in is consistent. Since the fluid flow rate is directly affected by the permeability, the stronger the permeability of the rock, the faster the fluid migration rate. Therefore, in the dominant channel with higher permeability, the fluidity is enhanced, and the fluid reaches the production well faster, which is manifested as a lower time lag coefficient τ.

[0170] Overall, this process provides a detailed analysis of the performance of the SV-DC model in describing well-to-well connectivity in a reservoir, and the results show that the SV-DC model is particularly effective in simulating the dynamic behavior of fluids in a reservoir, especially in its sensitivity in responding to pressure pulses. In addition, the model sensitively captures changes in the well-to-well connectivity coefficient λ and effectively reveals the effect of permeability on the migration velocity of fluids in the formation. The SV-DC model also quantifies this effect through the time lag coefficient τ, thereby representing the fluid transmission time from the injection well to the production well. These findings highlight the accuracy and applicability of the SV-DC model in analyzing well-to-well connectivity in a reservoir.

Claims

1. A method for constructing a model to dynamically calculate well connectivity parameters, characterized in that: The steps include: Step 100: establishing a material balance equation, a flow equation and a momentum equation describing the connectivity between the wells in sequence according to the production data of the injection wells and the production wells, and deriving a static capacitance model characterizing the connectivity between the injection wells and the production wells according to the balance equation, the flow equation and the momentum equation; Step 200: define state variables based on the static capacitance model, and fuse the state variables with the static capacitance model to construct a state variable model of the static capacitance model; Step 300: Based on the state variable model of the static capacitance model, the state variable model is subjected to extended Kalman filtering by using an extended Kalman filtering method to establish a dynamic capacitance model; Step 400: using the injection volume and liquid production volume data with the same time period as input parameters, and using the dynamic capacitance model to calculate and obtain the parameters of the state variables that dynamically change according to the corresponding time step; In step 200, the specific method of fusing the state variable with the static capacitance model to construct the state variable model is: Based on the static capacitance model, three state variables β are defined: j , ij , τ ij , these three state variables are described by the state vector to obtain the state vector equation: Among them, β j is the initial constant of imbalance; ij is the connectivity coefficient; τ ij is the time lag coefficient; x i (m) is a 3×1 state vector matrix; x(m) represents β j (m); x1(m) represents λ ij (m); x2(m) represents τ ij (m); Based on the state vector equation, the standard solution method proposed by Mendel is used to obtain the multi-injection and multi-collection state variable model: in, Representative Q j (n) is the total liquid production in the current time step; n xi (m) represents the system state noise; Q wi (m) is the injection volume of the ith injection well at the mth time step, and m = n-1; Among them, based on the state variable model and the static capacitance model, the observation matrix H of the corresponding time step is obtained by extending the Kalman filter, that is, including the state variable parameters of the corresponding time step.

2. A method for constructing a model to dynamically calculate well connectivity parameters according to claim 1, characterized in that: The state variables include three state variable parameters, namely, an initial imbalance constant, a connectivity coefficient from the injection well to the production well, and a time lag coefficient.

3. A method for constructing a model to dynamically calculate well connectivity parameters according to claim 2, characterized in that: In step 100, the specific method of deriving the static capacitance model is: Based on the principle that the total mass of the material between wells is constant, the equilibrium equation is established: Among them, C t is the compression coefficient; V ij is the pore volume; is the time rate of change of the average pressure; Q wi (t) is the injection volume of injection well i at time t; Q ij (t) is the flow rate of production well j at time t; Given the production index of a production well, the flow equation is established: Among them, J j is the productivity index of production well j; is the average pressure between injection well i and production well j; P wfj is the bottom hole flowing pressure of production well j; Based on the balance equation and flow equation, the momentum equation is established: in, is the rate of change of flow rate of production well j over time; is the rate of change of bottom hole flowing pressure with time; Since the bottom hole pressure fluctuation of the production well is much smaller than the liquid production, the simplified momentum equation is: Using the superposition principle and momentum simplified equation, the equation for calculating the total liquid production is: Among them, Q j (t) is the total liquid production of the production well; Q wi (ζ) is the injection volume of injection well i at time ζ; Discretize the total liquid production equation by time step to obtain the static capacitance model: Among them, Q j (n) is the total liquid production of the jth production well at the nth time step.

4. A method for constructing a model to dynamically calculate well connectivity parameters according to claim 3, characterized in that: In step 300, the specific method of performing extended Kalman filtering on the state variable model to establish a dynamic capacitance model is: Based on the mathematical model of the system state changing with time, the a priori estimation equation of the extended Kalman filter under discrete time is established: X(k|k-1)=FX(k-1|k-1)+n x (k-1); Among them, X(k|k-1) represents x(n) at time k, which is the predicted state of the system at time k; X(k-1|k-1) represents x(m) at time k, which is the optimal estimate of the state of the system at time k-1; F is the state matrix; n x (k-1) is the process noise; Based on the prior estimation equation, the error covariance prediction equation describing the uncertainty range of the system is established: P(k|k-1)=FP(k-1|k-1)F T +Q; Among them, P(k|k-1) is the optimal estimation error covariance at the previous moment; F T is the transposed matrix of F; Q is the process noise n x (k-1) covariance matrix; Based on the system state and its related state quantities, a measurement equation is established to describe the relationship between the system state and the observed value: Z(k)=HX(k)+V(k); Where Z(k) represents Q j (n) and P(n) are the actual measured values ​​at time k; V(k) is the measurement noise; n is the current time k; m is the previous time k-1; H is the observation matrix; Based on the observed and predicted values, a measurement residual equation is established to describe the difference between the observed and predicted values: y(k)=Z(k)-HX(k|k-1); Among them, HX(k|k-1) is the predicted measurement value; The Kalman gain equation is obtained based on the measurement residual equation: Based on the measurement residual equation and the Kalman gain equation, the optimal estimation equation is established: X(k|k)=X(k|k-1)+K g (k)[Z(k)-HX(k|k-1)]; Among them, X(k|k) is the optimal state estimate at time k; Update the error covariance of the optimal estimation equation to obtain the optimal error covariance equation: P(k|k)=[1-K g (k)H]P(k|k-1); Among them, the observation matrix H contains state variable parameters, the prior estimation equation and the error covariance prediction equation, which are cyclically updated with time steps through the optimal estimation equation and the optimal error covariance equation to obtain the observation matrix H of the corresponding time step, that is, the state variable parameters of the corresponding time step.

5. A method for constructing a model to dynamically calculate well connectivity parameters according to claim 4, characterized in that: The state matrix F is a 3N×3N Jacobian matrix, specifically: Among them, F x Determined by the number of wellheads, and defined as A i is the diagonal matrix of a single well.

6. A method for constructing a model to dynamically calculate well connectivity parameters according to claim 5, characterized in that: In step 400, the specific method of using the dynamic capacitance model to calculate and obtain the parameters of the state variables of the corresponding time step is: Let the static capacitance model be h, then: Then the calculation is: Based on the dynamic capacitance model, the observation matrix H of the corresponding time step is obtained, and the injection volume and liquid production volume data with the same time period are brought into each of the observation matrices H to obtain the connectivity coefficient λ according to the dynamic change of the corresponding time step. ij and the time lag coefficient τ ij .

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