A global sensitivity analysis method for pressure buildup well test design based on time series

Abstract

A global sensitivity analysis method for pressure recovery well test design based on time series belongs to the technical field of intelligent development of oil and gas fields. It is an improvement on the global sensitivity analysis method. This method considers the changes of all uncertain input parameters at the same time, adds the time-related variable t to the nonlinear relationship, and quantifies the contribution of each parameter to the total variance of model prediction at different times through sensitivity indicators. Specifically, when multiple key design parameters are uncertain parameters at the same time, the influence weight of each parameter changing with time is calculated, and the pressure recovery test is guided by the global sensitivity analysis results of multiple parameters. Quantitatively evaluate the influence of multiple uncertain parameters on pressure and pressure derivatives, and the influence of their interaction with other parameters on pressure, so as to determine the importance of parameters and provide a reference for the well shut-in time.

Description

Technical Field

[0001] The invention relates to a global sensitivity analysis method for pressure recovery well test design based on time series, belonging to the technical field of intelligent development of oil and gas fields. Background Art

[0002] Pressure recovery test and its well test interpretation are important means to understand the dynamics of oil and gas reservoirs. The dynamic changes of bottom hole pressure of oil and gas wells over time are monitored by storage pressure gauges, and the pressure is derived and fitted to obtain reservoir parameters. If the pressure recovery test time is short, the well test interpretation conditions are not met and the reservoir parameters cannot be interpreted; if the pressure recovery test time is long, the test cost will increase. Before the pressure recovery test, the well test design is carried out. Assuming that the reservoir parameters are known, the pressure recovery process is reversely simulated, which can guide the test work system and test time. Since it is impossible to accurately determine the reservoir parameters of the well test design, the selection of design parameters is mainly based on data such as well logging and core analysis, or by referring to the reservoir parameters of the adjacent wells, and assigning the design parameters of the well based on experience or correlation formulas. This makes the setting of design parameters subjective and blind; and due to the heterogeneity of reservoir characteristics, the reservoir parameters of the adjacent wells have poor guidance for the test wells. If the design parameters are not selected reasonably, it will greatly affect the accuracy of the well test design, mislead the test time of pressure recovery, and make the obtained test data poorly interpretable and the conclusions unreliable.

[0003] In the prior art, the following patent documents have been disclosed: US Patent Document US20220083873A1 discloses a system that may include a persistent storage containing training data related to oil well production, wherein the entries in the training data include time-independent input feature values ​​and time-dependent input feature values, respectively, both of which are mapped to the ground truth production value of the corresponding well at a specific time point, wherein the time-dependent input feature value includes the ground truth production value of the corresponding well at each earlier time point. The system may also include one or more processors, which are configured to: train a decision tree-based model with training data; provide a new time-independent input feature value and a new time-dependent input feature value for the well to the decision tree-based model; and receive, from the decision tree-based model, one or more predicted production values ​​of the well, wherein the one or more predicted production values ​​are generated by the decision tree-based model based on its internal structure, the new time-independent input feature value and the new time-dependent input feature value. In the system described in the patent document, the feature values ​​in the training data are mapped to the ground production value at a specific time point, and the specific relationship between the feature value and the downhole pressure data at a specific time point is not expressed.

[0004] Chinese patent document CN113657046A discloses a method, device, electronic equipment and medium for well test interpretation of complex structure wells in oil reservoirs. The method includes: determining the information of the change of physical properties of the zones caused by sand production in loose sandstone heavy oil reservoirs and the existing information of the seepage characteristics of the zones; determining the well test pressure curve information of the complex structure wells in loose sandstone heavy oil reservoirs based on the information of the change of physical properties of the zones and the information of the seepage characteristics of the zones; identifying the various flow stages required for the well test of the complex structure wells in loose sandstone heavy oil reservoirs based on the well test pressure curve information; performing flow analysis in stages, and determining the well test interpretation results of the complex structure wells in the oil reservoir based on the flow analysis results in stages and the pressure test data of the full test stage. The present application scheme is used to perform well test interpretation on such complex structure wells in loose sandstone heavy oil reservoirs by considering the comprehensive effects of the changes in physical properties of the zones caused by sand production and various complex seepage characteristics, and can be applied to any zone morphology and complex well types. This patent document uses an interpretation model, which determines reservoir parameters by identifying, interpreting and analyzing the flow stages of the test data, but does not describe how to determine the shut-in time for the pressure recovery test through well test design in order to accurately identify the flow stage.

[0005] In order to overcome the difficulties in selecting well test design parameters and reservoir heterogeneity, and to improve the guidance of well test design on the test work system and capacity prediction, different scholars have studied the problems faced through methods such as well test design parameter optimization and sensitivity analysis. For example, Zhang Jiaqing and Wang Jie et al. considered the impact of heterogeneity of parameters such as effective thickness and permeability on the well test design results, sorted out the tested data, and established the correlation formula for capacity prediction and well test design parameter optimization based on the correlation between core, well logging and well test interpretation formation parameters; Anton and Leonardis et al. established a numerical model and comprehensively considered factors such as wellbore conditions, reservoir properties, and boundary conditions, and determined the impact of design parameters on pressure and pressure derivatives through sensitivity analysis.

[0006] In summary, the current well test design parameter selection methods generally have large errors, especially when there are multiple uncontrollable variables at the same time, the sensitivity index of pressure and pressure derivative to each parameter is not accurately quantified and normalized. Therefore, how to find a method to quantify the contribution of uncertain parameters to the total variance of model prediction through sensitivity indicators is the technical problem that this technical field is concerned with solving. Summary of the invention

[0007] In order to solve the above technical problems, the present invention provides a global sensitivity analysis method for pressure buildup well test design based on time series.

[0008] The present invention also provides a readable storage medium for implementing the above-mentioned global sensitivity analysis method. Summary of the invention:

[0010] A global sensitivity analysis method for pressure recovery well test design based on time series is an improvement on the global sensitivity analysis (GSA) method. This method considers the changes of all uncertain input parameters at the same time, adds the time-related variable t to the nonlinear relationship, and quantifies the contribution of each parameter to the total variance of model prediction at different times through sensitivity indicators. Specifically, when multiple key design parameters are uncertain parameters at the same time, the influence weight of each parameter over time is calculated, and the pressure recovery test is guided by the global sensitivity analysis results of multiple parameters. The influence of multiple uncertain parameters on pressure and pressure derivatives, as well as the influence of their interaction with other parameters on pressure, are quantitatively evaluated to determine the importance of parameters and provide a reference for the well shut-in time.

[0011] The detailed technical scheme of the present invention is as follows:

[0012] A global sensitivity analysis method for pressure buildup well test design based on time series, characterized by comprising:

[0013] Step 101, establishing a pressure recovery interpretation model for a test well;

[0014] Step 102: Select the key design parameter type and value range;

[0015] Step 103, using the Sobol sampling method to obtain a combination sample of the key design parameters within a value range;

[0016] Step 104, setting the simulated shut-in time T, and using the pressure recovery interpretation model to calculate the pressure and pressure derivative of all combination samples of key design parameters;

[0017] Step 105, calculating a total effect index based on the pressure and pressure derivative of the time series;

[0018] Step 106: Determine the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods.

[0019] Preferably, according to the present invention, in step 101, the method for establishing a pressure recovery interpretation model for the test well includes:

[0020] Determine the pressure recovery interpretation model of the test well according to the oil and gas reservoir type, the inner boundary condition and the outer boundary condition, wherein the test well is one of an oil well or a gas well; the pressure recovery is the dynamic change process of the bottom hole pressure caused by the sudden shut-in of the test well from a stable production state; the determination of the interpretation model refers to "Modern Well Test Interpretation Method" written by Liao Xinwei (Petroleum Industry Press) and "Practical Modern Well Test Interpretation Method (Fifth Edition)" written by Liu Nengqiang (Petroleum Industry Press);

[0021] The oil and gas reservoir type includes one of a homogeneous oil / or gas reservoir, a dual-porosity oil / or gas reservoir, a dual-permeability oil / or gas reservoir, and a composite oil / or gas reservoir;

[0022] The internal boundary condition includes one of a vertical well, a deviated well, a horizontal well, a partial perforation, a finite conductivity fracture, and an infinite conductivity fracture;

[0023] The outer boundary condition includes one of an infinite boundary, a circular closed boundary, a circular constant pressure boundary, one / or two / or three impermeable boundaries, and one / or two / or three constant pressure boundaries;

[0024] The dependent variable and independent variable formulas of the explanatory model are obtained according to the actual test well conditions: the dependent variable is pressure p, and the independent variables include production, reservoir parameters, and time t; the production is the production before the well is shut in for the pressure recovery test.

[0025] According to the preferred embodiment of the present invention, the key design parameter types and value ranges selected in step 102 include:

[0026] The key design parameter types include: permeability k, skin coefficient S, well storage coefficient C;

[0027] When the outer boundary condition is a boundary type other than "infinite boundary", a boundary distance d is added in addition to the key design parameters. The boundary distance d is the distance of the boundary closest to the test well.

[0028] When the oil and gas reservoir type is "dual-porosity oil / or gas reservoir" or "dual-permeability oil / or gas reservoir", the energy storage ratio ω and crossflow coefficient λ are added in addition to the key design parameters;

[0029] The value range is determined according to the key design parameter type: permeability k∈[k L , k H ], skin coefficient S∈[S L , S H ], well storage coefficient C∈[C L , C H ], boundary distance d∈[d L d H ]; the energy storage ratio ω belongs to [ω L ,ω H ]; Crossflow coefficient λ∈[λ L , H ].

[0030] Preferably, according to the present invention, the method of obtaining the combined sample of the key design parameters within the value range by using the Sobol sampling method in step 103 includes:

[0031] The Sobol sampling described in this technical feature is used to obtain uniformly distributed random numbers to ensure the randomness of sample selection. The sampling principle refers to the document "Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index" published by Andrea Saltelli in Computer Physics Communications. Preferably, this technical feature can be implemented using the sobolset function in MATLAB software;

[0032] First, use the sobolset function to obtain an N×2m-dimensional Sobol sequence matrix, where m is the number of key design parameters; N is the number of samples for each key design parameter, and the minimum value of N is 200;

[0033] Select the first m columns as matrix A, select the last m columns as matrix B, and use the jth column in matrix B to replace the jth column in matrix A to construct m replacement matrices As shown in formulas (2) to (4), where a ij and b ij are all randomly generated sample points of the Sobol sequence, with a value range of [0, 1]; the Sobol sequence matrices A, B, The size of is N×m dimensions:

[0034]

[0035]

[0036]

[0037] According to the value range of the key design parameters in step 102, according to formula (5) and formula (6), the Sobol sequence matrices A, B, All elements in the , are converted into actual reservoir parameter samples, and the combined samples P, Q, As shown in formulas (7) to (9) respectively:

[0038] X ij =X jL +(X jH -X jL )×a ij (5)

[0039] X ij '=X jL +(X jH -XjL )×b ij (6)

[0040]

[0041]

[0042]

[0043] In formulas (5)-(9), X ij , X ij 'represents the design parameters X in the combined sample matrices P and Q respectively j The i-th sample of Each column in represents all the samples of a design parameter; the maximum value of i is N, and the maximum value of j is m; and They are the design parameters X j The lower and upper limits of

[0044] The design parameter X j represents the key design parameters selected in step 102;

[0045] In the combination sample matrix, the order of the design parameter types represented by each column can be changed, but the three matrices P, Q, The type of each column parameter must be consistent.

[0046] According to a preferred embodiment of the present invention, the method of setting the simulated shut-in time T in step 104 and calculating the pressure and pressure derivative of all combination samples of the key design parameters using the pressure recovery interpretation model includes:

[0047]

[0048]

[0049]

[0050] In formulas (10)-(12), F(P), F(Q), are sample matrices P, Q, The generated pressure matrix has N×n dimensions; p Pi 、p Qi 、p PQi The time-varying pressure generated for each row of design parameter samples is 1×n-dimensional; f is the pressure recovery interpretation model determined in step 101; t is time, which contains n time nodes t k :t1,t2,t3,…,t n , and the maximum value tn =T;

[0051] Pressure matrix F(P), F(Q), The pressure derivative variation with time is calculated using formula (13):

[0052]

[0053] In formula (13), L is the smoothing window length; p is the pressure; t k is the time node; p' is the pressure derivative.

[0054] Preferably, the method for calculating the total effect index based on the time series pressure and pressure derivative in step 105 includes:

[0055] According to formula (14), t k The residual matrix at time :

[0056]

[0057] In formula (14), t k The residual matrix at time t is m×1 in size, and each element corresponds to k The residual of the jth design parameter at time; Indicates t k The i-th row element of the pressure matrix F(P) at the moment is respectively related to the j-th pressure matrix Subtract the elements of the i-th row of in sequence;

[0058] As shown in formula (15), it is the residual matrix of all design parameters at each time node:

[0059]

[0060] In formula (15), the size of the matrix EX is m×n dimensions;

[0061] According to formula (16), the design parameters are calculated at t k The total effect index of the moment on the explanatory model:

[0062]

[0063] In formula (16), For m design parameters at t k The total effect index of time on the pressure in the explanatory model, the matrix size is m×1; The two pressure matrices F(P) and F(Q) are k The total variance at the moment, that is, the total variance of the kth column of the two matrices F(P) and F(Q);

[0064] The total effect index matrix of all design parameters at each time node:

[0065]

[0066] In formula (17), the element ST jk is the jth design parameter at t k Total effect index at time;

[0067] The jth row (ST j1 ST j2 … ST jn ) lines form the total effect index curve of the j-th design parameter on pressure;

[0068] The total effect index curves of all design parameters are superimposed to form a total effect index area diagram of pressure;

[0069] The pressure derivative matrix obtained by formula (13) is used to replace the pressure matrix in formulas (14) to (17) to obtain the total effect index curve of each design parameter on the pressure derivative and the total effect index area diagram of the pressure derivative.

[0070] Preferably, according to the present invention, step 106 determines the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods, including:

[0071] The shut-in time for the pressure recovery test is set to T max , where T max Not greater than the time T in step 104;

[0072] The shut-in time T max The minimum value of satisfies the following conditions in the pressure total effect index area diagram and the pressure derivative total effect index area diagram:

[0073] S1: For all the explanation models in step 101, T max Within the time, there is a specific period that makes the fluctuation range of the total effect index of all design parameters on pressure no more than 0.1, and the proportion of the total effect index of permeability on pressure derivative is no less than 0.9:

[0074] If T max=T, the conditions that the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the proportion of the total effect index of permeability on pressure derivative is not less than 0.9 are not met, then the simulation time T in step 104 is extended, and steps 104 to 106 are repeated until the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the total effect index of permeability on pressure derivative is not less than 0.9 is met, and the specific period is 1 / 3 of a logarithmic period, and the logarithmic period is the distance between two adjacent 10-fold relationship values ​​in the logarithmic coordinate scale;

[0075] S2: For the outer boundary condition described in step 101, which is other boundary types than "infinite boundary", while satisfying step S1, the total effect index of the boundary distance d on the pressure derivative reaches the maximum value and then decreases to within 0.1, which meets the requirements;

[0076] S3: When the oil and gas reservoir type described in step 101 is "double-porosity oil / or gas reservoir" or "double-permeability oil / or gas reservoir", then while satisfying step S1, the total effect index of the energy storage ratio ω and the crossflow coefficient λ on the pressure derivative respectively reaches the maximum value and then decreases to within 0.1 to meet the requirements.

[0077] A readable storage medium loaded with the above method includes: a non-transitory computer readable medium includes machine executable instructions, and the machine executable instructions are used to execute the above method.

[0078] The beneficial effects of the present invention are:

[0079] When the method of the present invention designs a well test for a pressure recovery test, when there are multiple uncertain design parameters, each parameter not only affects the pressure or pressure derivative individually, but is also affected by the interaction of other parameters. The global sensitivity analysis method based on time series can calculate the total effect index of multiple uncontrollable variables; by calculating the global sensitivity index at different time nodes, the influence of different parameters on pressure or pressure derivatives at each stage can be quantitatively described.

[0080] The present invention is a global sensitivity analysis method based on time series, which is applied to well test design and testing of oil and gas wells, reduces the subjectivity and blindness of test plans, and improves the validity of test data and the credibility of interpretation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 An operation flow chart of a global sensitivity analysis method for pressure buildup well test design based on time series provided by the present invention;

[0082] Figure 2Schematic diagram explaining the range of pressure and pressure derivative changes over time for all samples of key design parameters in the model for the “homogeneous model + vertical well + infinite boundary”;

[0083] Figure 3 is a schematic diagram of the total effect index curve and area diagram of each key design parameter on pressure in the "homogeneous model + vertical well + infinite boundary" interpretation model over time, where: Figure 3a is the total effect index curve; Figure 3b is the total effect index area plot;

[0084] Figure 4 is a schematic diagram of the total effect index curve and area diagram of each key design parameter on the pressure derivative in the "homogeneous model + vertical well + infinite boundary" interpretation model over time, where: Figure 4a is the total effect index curve; Figure 4b is the total effect index area plot;

[0085] Figure 5 Design the range of pressure and pressure derivative changes over time for all key design parameter samples for a well pressure recovery test at a certain site;

[0086] Figure 6 shows the total effect index curve and area diagram of each key design parameter on pressure in the pressure recovery test design of a certain oil well on site over time, where: Figure 6a is the total effect index curve; Figure 6b is the total effect index area plot;

[0087] Figure 7 shows the total effect index curve and area diagram of each key design parameter on the pressure derivative in the pressure recovery test design of a certain oil well on site over time, where: Figure 7a is the total effect index curve; Figure 7b This is an area chart of the total effect index. DETAILED DESCRIPTION

[0088] The present invention will be described in detail below with reference to the embodiments and the accompanying drawings, but is not limited thereto.

[0089] Embodiment 1,

[0090] like Figure 1 shown.

[0091] A global sensitivity analysis method for pressure buildup well test design based on time series, characterized by comprising:

[0092] Step 101, establishing a pressure recovery interpretation model for a test well;

[0093] Step 102: Select the key design parameter type and value range;

[0094] Step 103, using the Sobol sampling method to obtain a combination sample of the key design parameters within a value range;

[0095] Step 104, setting the simulated shut-in time T, and using the pressure recovery interpretation model to calculate the pressure and pressure derivative of all combination samples of key design parameters;

[0096] Step 105, calculating a total effect index based on the pressure and pressure derivative of the time series;

[0097] Step 106: Determine the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods.

[0098] In step 101, the method for establishing a pressure recovery interpretation model for a test well includes:

[0099] Determine the pressure recovery interpretation model of the test well according to the oil and gas reservoir type, the inner boundary condition and the outer boundary condition, wherein the test well is one of an oil well or a gas well; the pressure recovery is the dynamic change process of the bottom hole pressure caused by the sudden shut-in of the test well from a stable production state; the determination of the interpretation model refers to "Modern Well Test Interpretation Method" written by Liao Xinwei (Petroleum Industry Press) and "Practical Modern Well Test Interpretation Method (Fifth Edition)" written by Liu Nengqiang (Petroleum Industry Press);

[0100] The oil and gas reservoir type includes one of a homogeneous oil / or gas reservoir, a dual-porosity oil / or gas reservoir, a dual-permeability oil / or gas reservoir, and a composite oil / or gas reservoir;

[0101] The internal boundary condition includes one of a vertical well, a deviated well, a horizontal well, a partial perforation, a finite conductivity fracture, and an infinite conductivity fracture;

[0102] The outer boundary condition includes one of an infinite boundary, a circular closed boundary, a circular constant pressure boundary, one / or two / or three impermeable boundaries, and one / or two / or three constant pressure boundaries;

[0103] The dependent variable and independent variable formulas of the explanatory model are obtained according to the actual test well conditions: the dependent variable is pressure p, and the independent variables include production, reservoir parameters, and time t; the production is the production before the well is shut in for the pressure recovery test.

[0104] The structure of the explanatory model is shown in formula (1), where the dependent variable Y represents pressure or pressure derivative; the independent variables include reservoir parameters X i and time parameter t.

[0105] Y=f(X1,X2,X3,…,X m , t) (1)

[0106] The data model established by combining reservoir type, boundary type and well model is further solved to obtain the solution of bottom hole pressure in Laplace space after Laplace transformation. Finally, the interpretation model is obtained through Stehfest numerical inversion and superposition principle.

[0107] The key design parameter types and value ranges selected in step 102 include:

[0108] The key design parameter types include: permeability k, skin coefficient S, well storage coefficient C;

[0109] When the outer boundary condition is a boundary type other than "infinite boundary", a boundary distance d is added in addition to the key design parameters. The boundary distance d is the distance of the boundary closest to the test well.

[0110] When the oil and gas reservoir type is "dual-porosity oil / or gas reservoir" or "dual-permeability oil / or gas reservoir", the energy storage ratio ω and crossflow coefficient λ are added in addition to the key design parameters;

[0111] The value range is determined according to the key design parameter type: permeability k∈[k L , k H ], skin coefficient S∈[S L , S H ], well storage coefficient C∈[C L , C H ], boundary distance d∈[d L d H ]; the energy storage ratio ω belongs to [ω L ,ω H ]; Crossflow coefficient λ∈[λ L , H ].

[0112] Generally, the interpretation model of "homogeneous model + vertical well + infinite boundary" has design parameters including permeability k, skin coefficient S, and well storage coefficient C; the interpretation model of "homogeneous model + vertical well + impermeable boundary (constant pressure boundary)" has design parameters including permeability k, skin coefficient S, well storage coefficient C, and boundary distance d; the interpretation model of "dual porosity medium model + vertical well + infinite boundary" has design parameters including permeability k, skin coefficient S, well storage coefficient C, energy storage ratio ω, and cross-flow coefficient λ. For specific well test interpretation models and design parameters, please refer to the Technical Specifications for Oilfield Well Test SY / T 6172-2006 and the Technical Specifications for Natural Gas Well Test SY / T5440-2019.

[0113] The range of design parameters needs to refer to the reservoir parameters of adjacent wells around the test well, or be determined based on logging data, core analysis, wellbore volume, bottom hole pollution, etc.

[0114] The permeability k uses the permeability interpreted by well logging or the permeability of core analysis as the middle value, and takes the upper limit and lower limit values ​​according to a certain ratio; if there is no well logging interpretation or core analysis, the middle value refers to the permeability value of the adjacent wells around the test well, and the certain ratio is 30%;

[0115] The well storage coefficient C determines the middle value according to the test wellbore volume and the fluid compression coefficient, and takes the upper and lower limits according to a certain ratio; the certain ratio is 30%; the skin coefficient S is determined according to the bottom hole pollution. If the engineering factors cause the drilling fluid to invade the formation, the middle value of the skin coefficient is 5, and the middle value of the skin coefficient is 0 in other cases. The upper and lower limits of the skin coefficient are set to the middle value ±5; the middle values ​​of other design parameters refer to the average values ​​of adjacent wells or wells in the same layer in this area, and the upper and lower limits are determined according to 30%.

[0116] The method of obtaining the combined sample of the key design parameters within the value range by using the Sobol sampling method in step 103 includes:

[0117] The Sobol sampling described in this technical feature is used to obtain uniformly distributed random numbers to ensure the randomness of sample selection. The sampling principle refers to the document "Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index" published by Andrea Saltelli in Computer Physics Communications. Preferably, this technical feature can be implemented using the sobolset function in MATLAB software;

[0118] First, use the sobolset function to obtain an N×2m-dimensional Sobol sequence matrix, where m is the number of key design parameters; N is the number of samples for each key design parameter, and the minimum value of N is 200;

[0119] Select the first m columns as matrix A, select the last m columns as matrix B, and use the jth column in matrix B to replace the jth column in matrix A to construct m replacement matrices As shown in formulas (2) to (4), where a ij and b ij are all randomly generated sample points of the Sobol sequence, with a value range of [0, 1]; the Sobol sequence matrices A, B, The size of is N×m dimensions:

[0120]

[0121]

[0122]

[0123] According to the value range of the key design parameters in step 102, according to formula (5) and formula (6), the Sobol sequence matrices A, B, All elements in the , are converted into actual reservoir parameter samples, and the combined samples P, Q, As shown in formulas (7) to (9) respectively:

[0124] X ij =X jL +(X jH -X jL )×a ij (5)

[0125] X ij '=X jL +(X jH -X jL )×b ij (6)

[0126]

[0127]

[0128]

[0129] In formulas (5)-(9), X ij , X ij 'represents the design parameters X in the combined sample matrices P and Q respectively j The i-th sample of Each column in represents all the samples of a design parameter; the maximum value of i is N, and the maximum value of j is m; and They are the design parameters X j The lower and upper limits of

[0130] The design parameter X j represents the key design parameters selected in step 102;

[0131] In the combination sample matrix, the order of the design parameter types represented by each column can be changed, but the three matrices P, Q, The type of each column parameter must be consistent.

[0132] According to a preferred embodiment of the present invention, the method of setting the simulated shut-in time T in step 104 and calculating the pressure and pressure derivative of all combination samples of the key design parameters using the pressure recovery interpretation model includes:

[0133]

[0134]

[0135]

[0136] In formulas (10)-(12), F(P), F(Q), are sample matrices P, Q, The generated pressure matrix has N×n dimensions; p Pi 、p Qi 、p PQi The time-varying pressure generated for each row of design parameter samples is 1×n-dimensional; f is the pressure recovery interpretation model determined in step 101; t is time, which contains n time nodes t k :t1,t2,t3,…,t n , and the maximum value t n =T;

[0137] Pressure matrix F(P), F(Q), The pressure derivative variation with time is calculated using formula (13):

[0138]

[0139] In formula (13), L is the smoothing window length; p is the pressure; t k is the time node; p' is the pressure derivative.

[0140] like Figure 2 The figure shows the range of pressure and pressure derivative changes over time for all key design parameter samples, taking the "homogeneous model + vertical well + infinite boundary" interpretation model as an example. It can be seen that the uncertainty of the key design parameter samples causes the uncertainty of the pressure and pressure derivative sample curves within a certain range, providing a sample reference for the calculation of the total effect index.

[0141] Preferably, the method for calculating the total effect index based on the time series pressure and pressure derivative in step 105 includes:

[0142] According to formula (14), t k The residual matrix at time :

[0143]

[0144] In formula (14), t k The residual matrix at time t is m×1 in size, and each element corresponds to k The residual of the jth design parameter at time; Indicates t k The i-th row element of the pressure matrix F(P) at the moment is respectively related to the j-th pressure matrix Subtract the elements of the i-th row of in sequence;

[0145] As shown in formula (15), it is the residual matrix of all design parameters at each time node:

[0146]

[0147] In formula (15), the size of the matrix EX is m×n dimensions;

[0148] According to formula (16), the design parameters are calculated at t k The total effect index of the moment on the explanatory model:

[0149]

[0150] In formula (16), For m design parameters at t k The total effect index of time on the pressure in the explanatory model, the matrix size is m×1; The two pressure matrices F(P) and F(Q) are k The total variance at the moment, that is, the total variance of the kth column of the two matrices F(P) and F(Q);

[0151] The total effect index matrix of all design parameters at each time node:

[0152]

[0153] In formula (17), the element ST jk is the jth design parameter at t k Total effect index at time;

[0154] The jth row (ST j1 ST j2 … ST jn ) are connected to form the total effect index curve of the jth design parameter on pressure, as shown in Figure 3(a). The total effect index (i.e., the degree of influence) of different design parameters on pressure changes with time. Therefore, the influence of a certain parameter on pressure at a specific moment can be determined under the joint influence of multiple parameters.

[0155] The pressure total effect index curves of all design parameters are superimposed to form a pressure total effect index area diagram, as shown in Figure 3(b). The total effect index area diagram can be used to determine the change of a certain parameter over time and its proportion at a certain moment. This can intuitively determine the influence of each parameter on the pressure at different time stages, which can be used to assist in determining the appropriate pressure recovery time.

[0156] The pressure derivative matrix obtained by formula (13) is used to replace the pressure matrix in formulas (14) to (17) to obtain the total effect index curve of each design parameter on the pressure derivative. As shown in Figure 4(a), the total effect index (i.e., the degree of influence) of different design parameters on the pressure derivative changes with time. Therefore, when multiple parameters have a common influence, the influence of a certain parameter on the pressure derivative at a specific time can be determined;

[0157] The total effect index curves of the pressure derivatives of all design parameters are superimposed to form a total effect index area diagram of the pressure derivative, as shown in Figure 4(b). The total effect index area diagram can be used to determine the change of a certain parameter over time and its proportion at a certain moment. This can intuitively determine the degree of influence of each parameter on the pressure derivative at different time stages, so as to determine the appropriate pressure recovery time.

[0158] Step 106 determines the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods, including:

[0159] The shut-in time for the pressure recovery test is set to T max , where T max Not greater than the time T in step 104;

[0160] The shut-in time T max The minimum value of satisfies the following conditions in the pressure total effect index area diagram and the pressure derivative total effect index area diagram:

[0161] S1: For all the explanation models in step 101, T max Within the time, there is a specific period that makes the fluctuation range of the total effect index of all design parameters on pressure no more than 0.1, and the proportion of the total effect index of permeability on pressure derivative is no less than 0.9:

[0162] If T max=T, the conditions that the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the proportion of the total effect index of permeability on pressure derivative is not less than 0.9 are not met, then the simulation time T in step 104 is extended, and steps 104 to 106 are repeated until the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the total effect index of permeability on pressure derivative is not less than 0.9 is met, and the specific period is 1 / 3 of a logarithmic period, and the logarithmic period is the distance between two adjacent 10-fold relationship values ​​in the logarithmic coordinate scale;

[0163] S2: For the outer boundary condition described in step 101, which is other boundary types than "infinite boundary", while satisfying step S1, the total effect index of the boundary distance d on the pressure derivative reaches the maximum value and then decreases to within 0.1, which meets the requirements;

[0164] S3: When the oil and gas reservoir type described in step 101 is "double-porosity oil / or gas reservoir" or "double-permeability oil / or gas reservoir", then while satisfying step S1, the total effect index of the energy storage ratio ω and the crossflow coefficient λ on the pressure derivative respectively reaches the maximum value and then decreases to within 0.1 to meet the requirements.

[0165] A readable storage medium loaded with the above method includes: a non-transitory computer readable medium includes machine executable instructions, and the machine executable instructions are used to execute the above method.

[0166] Embodiment 2,

[0167] A readable storage medium loaded with the method as described in Example 1 includes: machine executable instructions included on a non-volatile computer readable medium, wherein the machine executable instructions are used to execute the above method.

[0168] Now, the process of designing the actual oil well test in combination with the above embodiment is as follows:

[0169] The global sensitivity analysis method for pressure buildup well test design based on time series described in Example 1 is adopted, and the specific steps are as follows:

[0170] Step 101: The test well is a vertical well, the reservoir lithology is sandstone, and the structural map shows that there is a fault about 200m near the well. The interpretation model is selected as "homogeneous reservoir + vertical well + an impermeable boundary":

[0171] 1) The model of "homogeneous reservoir + vertical well" is expressed as:

[0172]

[0173] In formula (18), represents the solution of the bottom hole pressure in Laplace space; K0(x) and K1(x) are zero-order and first-order imaginary Bessel functions, respectively; u is the Laplace variable; S is the skin coefficient; C D is the dimensionless well-reservoir coefficient. Obtained by Stehfest numerical inversion The solution p in real space wDi ;

[0174] 2) The “one impermeable boundary” model is expressed as:

[0175]

[0176] In formula (19), p wDb represents the bottom hole pressure caused by boundary effect; Ei(-x) is the exponential integral function; d D is the dimensionless boundary distance, d D =d / r w ; d is the boundary distance; r w is the wellbore radius; t D is dimensionless time;

[0177] 3) Through the superposition principle, the interpretation model (bottom hole pressure) of "homogeneous reservoir + vertical well + an impermeable boundary" is obtained as follows:

[0178] p wD =p wDi +p wDb (20)

[0179] Step 102, determine the key design parameters based on the interpretation model: permeability k, skin coefficient S, well storage coefficient C, and boundary distance d. This oil well has no logging and core analysis data. The middle value of permeability k refers to the adjacent well; the middle value of skin coefficient S is 0; the middle value of well storage coefficient C is calculated based on the wellbore volume and oil compression coefficient; the middle value of boundary distance d is 200m. The middle value and upper and lower limit ranges of each design parameter are shown in Table 1:

[0180] Table 1: The median value and upper and lower limits of each design parameter

[0181]

[0182]

[0183] Step 103, using the Sobol sampling method to obtain the combination samples of each design parameter, the number of samples N = 200, and a total of two 200×4-dimensional matrices and four 200×4-dimensional replacement matrices are obtained;

[0184] Step 104: Set the shut-in time T = 1000 hours, and use the pressure recovery interpretation model to calculate the pressure and pressure derivative of all combination samples of key design parameters, such as Figure 5 As shown;

[0185] Step 105, take 70 points at equal logarithmic time intervals, and calculate the index curve of the total effect of each key design parameter on pressure based on the time series, such as Figure 6a As shown in Figure 1, it can be seen that the total effect index of the well storage coefficient C is the largest in the initial stage, and then the skin coefficient S and permeability k begin to dominate. The total effect index curves of each design parameter are superimposed to obtain the pressure total effect index area diagram, as shown in Figure 1. Figure 6b As shown, it can be seen that the proportion of the total effect index of each design parameter on pressure changes significantly between 0.005 hours and 0.2 hours, and the proportion of permeability k and skin coefficient S gradually stabilizes in the later period. The total effect index proportion of boundary distance d is less than 0.05 in the entire shut-in simulation stage.

[0186] Calculate the total effect index curve of each key design parameter on the pressure derivative based on the time series, such as Figure 7a As shown, it can be seen that the total effect index of the well storage coefficient C is the largest at the beginning, and then the total effect indexes of the skin coefficient S, permeability k, and boundary distance d successively reach the maximum value, and finally the total effect index of the permeability k gradually increases to above 0.95. The total effect index curves of each design parameter are superimposed to obtain the pressure derivative total effect index area diagram, as shown in Figure 7b As shown, it can be clearly seen that the influence ratio of each parameter on the total effect index of pressure derivative in each stage is used to determine the appropriate pressure recovery time;

[0187] Step 106: Determine the appropriate pressure recovery test time T according to the total effect index of each key design parameter in different time periods. max :

[0188] In the area diagram of the total effect index of pressure and pressure derivative, the proportion of the total effect index of permeability on pressure derivative reaches 0.9 at 1.4 hours, and in the subsequent 1 / 3 logarithmic period (i.e., 1.4 hours to 3.0 hours), the proportion is not less than 0.9; the total effect index of each design parameter on pressure in the same logarithmic period (i.e., 1.4 hours to 3.0 hours) has a fluctuation range of no more than 0.1;

[0189] The total effect index of the boundary distance d on the pressure derivative reaches the maximum value at 30.2 hours and decreases to less than 0.1 at 295 hours. The pressure recovery test time T max Set to 295 hours;

[0190] A global sensitivity analysis method is designed based on time series pressure recovery well testing to guide the pressure recovery test system and shut-in time of the test well.

Claims

1. A global sensitivity analysis method for pressure buildup well test design based on time series, characterized in that: include: Step 101, establishing a pressure recovery interpretation model for a test well; Step 102: Select the key design parameter type and value range; Step 103, using the Sobol sampling method to obtain a combination sample of the key design parameters within a value range; Step 104, setting the simulated shut-in time T, and using the pressure recovery interpretation model to calculate the pressure and pressure derivative of all combination samples of key design parameters; Step 105, calculating a total effect index based on the pressure and pressure derivative of the time series; The method for calculating the total effect index based on the time series of pressure and pressure derivatives includes: According to formula (14), t k The residual matrix at time : In formula (14), t k The residual matrix at time t is m×1 in size, and each element corresponds to k The residual of the jth design parameter at time; Indicates t k The i-th row element of the pressure matrix F(P) at the moment is respectively related to the j-th pressure matrix Subtract the elements of the i-th row of in sequence; As shown in formula (15), it is the residual matrix of all design parameters at each time node: In formula (15), the size of the matrix EX is m×n dimensions; According to formula (16), the design parameters are calculated at t k The total effect index of the moment on the explanatory model: In formula (16), For m design parameters at t k The total effect index of time on the pressure in the explanatory model, the matrix size is m×1; The two pressure matrices F(P) and F(Q) are k The total variance at the moment, that is, the total variance of the kth column of the two matrices F(P) and F(Q); The total effect index matrix of all design parameters at each time node: In formula (17), the element ST jk is the jth design parameter at t k Total effect index at time; The jth row (ST j1 ST j2 …ST jn ) lines form the total effect index curve of the j-th design parameter on pressure; The total effect index curves of all design parameters are superimposed to form a total effect index area diagram of pressure; The pressure derivative matrix obtained by formula (13) is used to replace the pressure matrix in formulas (14) to (17) to obtain the total effect index curve of each design parameter on the pressure derivative and the total effect index area diagram of the pressure derivative; Step 106: Determine the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods.

2. A global sensitivity analysis method for pressure buildup well test design based on time series according to claim 1, characterized in that: In step 101, the method for establishing a pressure recovery interpretation model for a test well includes: The pressure recovery interpretation model of the test well is determined according to the oil and gas reservoir type, internal boundary conditions and external boundary conditions.

3. A global sensitivity analysis method for pressure buildup well test design based on time series according to claim 2, characterized in that: The key design parameter types and value ranges selected in step 102 include: The key design parameter types include: permeability k, skin coefficient S, well storage coefficient C; When the outer boundary condition is other than "infinite boundary", the boundary distance d is added in addition to the key design parameters; When the oil and gas reservoir type is "dual-porosity oil / or gas reservoir" or "dual-permeability oil / or gas reservoir", the energy storage ratio ω and crossflow coefficient λ are added in addition to the key design parameters; The value range is determined according to the key design parameter type: permeability k∈[k L , k H ], skin coefficient S∈[S L , S H ], well storage coefficient C∈[C L , C H ], boundary distance d∈[d L ,d H ]; the energy storage ratio ω belongs to [ω L ,ω H ]; Crossflow coefficient λ∈[λ L , H ].

4. The global sensitivity analysis method for pressure buildup well test design based on time series according to claim 1 is characterized in that: The method of obtaining the combined sample of the key design parameters within the value range by using the Sobol sampling method in step 103 includes: First, use the sobolset function to obtain an N×2m-dimensional Sobol sequence matrix, where m is the number of key design parameters; N is the number of samples for each key design parameter; Select the first m columns as matrix A, select the last m columns as matrix B, and use the jth column in matrix B to replace the jth column in matrix A to construct m replacement matrices As shown in formulas (2) to (4), where a ij and b ij are all randomly generated sample points of the Sobol sequence, with a value range of [0, 1]; the Sobol sequence matrices A, B, The size of is N×m dimensions: According to the value range of the key design parameters in step 102, according to formula (5) and formula (6), the Sobol sequence matrices A, B, All elements in the , are converted into actual reservoir parameter samples, and the combined samples P, Q, As shown in formulas (7) to (9) respectively: In formulas (5)-(9), X ij , X ij 'represents the design parameters X in the combined sample matrices P and Q respectively j The i-th sample of Each column in represents all the samples of a design parameter; the maximum value of i is N, the maximum value of j is m; X jL and X jH They are the design parameters X j The lower and upper limits of The design parameter X j represents the key design parameters selected in step 102 .

5. The global sensitivity analysis method for pressure buildup well test design based on time series according to claim 1 is characterized in that: Step 104 sets the simulated shut-in time T, and uses the pressure recovery interpretation model to calculate the pressure and pressure derivative of all combination samples of the key design parameters, including: In formulas (10)-(12), F(P), F(Q), are sample matrices P, Q, The generated pressure matrix has N×n dimensions; p Pi 、p Qi 、p PQi The time-varying pressure generated for each row of design parameter samples is 1×n-dimensional; f is the pressure recovery interpretation model determined in step 101; t is time, which contains n time nodes t k :t1,t2,t3,…,t n , and the maximum value t n =T; Pressure matrix F(P), F(Q), The pressure derivative variation with time is calculated using formula (13): In formula (13), L is the smoothing window length; p is the pressure; t k is the time node; p' is the pressure derivative.

6. A global sensitivity analysis method for pressure buildup well test design based on time series according to claim 3, characterized in that: Step 106 determines the appropriate pressure recovery test time according to the total effect index of each key design parameter in different time periods, including: The shut-in time for the pressure recovery test is set to T max , where T max Not greater than the time T in step 104; The shut-in time T max The minimum value of satisfies the following conditions in the pressure total effect index area diagram and the pressure derivative total effect index area diagram: S1: For all the explanation models in step 101, T max Within the time, there is a specific period that makes the fluctuation range of the total effect index of all design parameters on pressure no more than 0.1, and the proportion of the total effect index of permeability on pressure derivative is no less than 0.9: If T max =T, the conditions that the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the proportion of the total effect index of permeability on pressure derivative is not less than 0.9 are not met, then the simulation time T in step 104 is extended, and steps 104 to 106 are repeated until the fluctuation range of the total effect index of all design parameters on pressure is not greater than 0.1 and the total effect index of permeability on pressure derivative is not less than 0.9 is met, and the specific period is 1 / 3 of a logarithmic period, and the logarithmic period is the distance between two adjacent 10-fold relationship values ​​in the logarithmic coordinate scale; S2: For other boundary types other than "infinite boundary" in the outer boundary condition described in step 101, while satisfying step S1, the total effect index of the boundary distance d on the pressure derivative reaches a maximum value and then decreases to within 0.1, which meets the requirements; S3: When the oil and gas reservoir type described in step 101 is "dual-porosity oil / or gas reservoir" or "dual-permeability oil / or gas reservoir", while satisfying step S1, the total effect index of the energy storage ratio ω and the crossflow coefficient λ on the pressure derivative respectively reaches the maximum value and then decreases to within 0.1 to meet the requirements.

7. A readable storage medium loaded with the method according to any one of claims 1 to 6, comprising: The non-transitory computer readable medium includes machine executable instructions for performing the above-described method.

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