A dynamic prediction method for injection and production output of oil and gas fields based on linear dynamic system

Abstract

The present invention proposes a method for dynamic prediction of injection and production of oil and gas fields based on a linear dynamic system. The method is aimed at low permeability oil and gas fields with water injection as the main driving method. The method includes: establishing a linear dynamic system (LDS) production prediction model based on the control material balance equation of the entire reservoir of the water-driven oil and gas field; using the EM method to estimate the model parameters in the LDS production prediction model; collating and dividing the dynamic data, dividing the data set into a training set and a test set according to a certain ratio; initializing the model parameters and calculating the parameters, integrating the prediction results and calculating the relative error. The introduction of hidden variables in the LDS production prediction model in this method better characterizes the injection-production relationship in actual production, and can make a more accurate prediction of the monthly production of low permeability oil and gas reservoirs.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas exploitation, and more specifically, to a method for dynamically predicting the injection and production output of an oil and gas field based on a linear dynamic system. Background Art

[0002] Water flooding is a widely used method in the development of oil and gas reservoirs. When dynamically predicting the process of water flooding gas and oil production in low permeability oil and gas reservoirs, traditional dynamic prediction methods, such as water flooding characteristic curve method, material balance equation prediction method, reservoir numerical simulation method, etc., are not very ideal in low permeability reservoirs. The main reason is that traditional methods are mainly applicable to high permeability reservoirs and cannot characterize the long-term transient flow in low permeability reservoirs. At present, low permeability oil and gas reservoirs are widespread and have abundant reserves. The prediction of their production is the focus of future research.

[0003] In the field of dynamic prediction of oil and gas field production with water injection as the main production driving mode, the capacitance model (CM) proposed by AA Youself and P. Gentil et al. in 2005 is currently widely used. This model is developed on the basis of the well connectivity model proposed by Alejandro Albertoni and Larry W. Lake. The capacitance model quantifies the connectivity between vertical wells, while taking into account the rock compressibility and fluid transmission in the reservoir, and better explains the changing relationship between injection rate and production rate. Feilong Liu and Jerry M. Mendel et al. used the extended Kalman filter (EKF) to predict the injection-production relationship (IPR) between multiple injection wells and a single production well based on the measured production and injection rate data. This study used a continuous-time unimodal function to simulate the instantaneous impulse response between the injection well and the production well. This method can characterize the flow behavior of the fluid between the injection and production wells. Mohammad Soroush considered the impact of production operations on the final production based on the traditional capacitance model. Zequn Zhang, Heng Li and others expanded the capacitance model in 2015 and established a multilayer capacitance resistance model (MLCRM) for predicting water drive performance in stratified reservoirs. At the same time, the ensemble Kalman filter (EnKF) method was used to estimate the connectivity coefficient and well index of each layer in the multilayer capacitance resistance model (MLCRM). In the prior art, there are few applications of linear dynamic systems (LDS) in the field of oil and gas production technology. The search for published patents only obtained a method for collaborative monitoring of spill risk in the drilling process of oil and gas wells (202110160988.8), which belongs to the field of drilling technology and is significantly different from the technical field to which the present invention is to be applied.

[0004] The models in the above-mentioned prior art generally have common shortcomings: the parameters cannot be learned through data, and these parameters need to be set to fixed values ​​in advance, which usually reduces the prediction accuracy, especially in low-permeability reservoirs. In addition, the prior art cannot make a good representation of the instantaneous flow of fluids in water-driven oil and gas reservoirs, and cannot solve the technical problem of accurately predicting the production in low-permeability water-driven oil and gas reservoirs. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problem that the above existing methods cannot accurately predict the production in low-permeability water-driven oil and gas reservoirs, and to provide a method for dynamically predicting the injection and production production of oil and gas fields based on a linear dynamic system.

[0006] The present invention is realized by the following technical scheme: a method for dynamic prediction of oil and gas field injection and production output based on a linear dynamic system, comprising the following steps:

[0007] Step S1: Based on the control material balance equation of the entire reservoir of the water-driven oil and gas field, a linear dynamic system (LDS) production prediction model is established;

[0008] Step S2: using the EM (Expectation Maximization) method to estimate the model parameters in the linear dynamic system (LDS) production prediction model;

[0009] Step S3: organize and divide the dynamic data, divide the data set into training set and test set according to a certain ratio;

[0010] Step S4: initialization of the model parameters and parameter calculation, integration of prediction results and calculation of relative errors;

[0011] In a preferred embodiment of the present invention, in step S1, during the exploitation of the water-driven oil and gas field, the controlling material balance equation of the entire reservoir is:

[0012]

[0013] Among them, c t is the total compressibility, MPa -1 ; V p is the pore volume of the reservoir, m 3 ; is the average rate of change of reservoir pressure, MPa / t; i(t) and q(t) represent the total injection rate and production rate at time t, respectively, m 3 / t.

[0014] In a preferred embodiment of the present invention, in step S1, the linear dynamic system (LDS) production prediction model mainly includes three parts:

[0015] Hidden state equation: z n+1 =Az n +Bu n +w,w~N(0,Q)

[0016] Observation equation: x n =Hz n +Cu n +v,v~N(0,R)

[0017] The initial state of the model:

[0018] Where s is the noise coefficient of the initial state variable, dimensionless; w is the system noise coefficient, dimensionless; v is the observation noise coefficient, dimensionless; Q, R, V 0 are the covariance matrix coefficients of w, v, and s, respectively, dimensionless.

[0019] In a preferred embodiment of the present invention, in step S2, the iterative update of the model parameters is divided into two steps. The first step is to obtain the predicted values ​​of the data after manually initializing the model parameters; the second step is to estimate the model parameters in reverse using the predicted values ​​of the obtained data; all calculation processes are implemented through Python programming.

[0020] In a preferred embodiment of the present invention, in step S3, the ratio of the training set to the test set is 7:3.

[0021] In a preferred embodiment of the present invention, in step S4, the relative errors between the training set and the test set are less than 5% and 10% respectively, which meets the accuracy requirement; the final monthly output forecast value is equal to the average value of the 10 forecast results.

[0022] Compared with the prior art, the present invention has at least the following advantages: the present invention aims at low-permeability oil and gas fields with water injection as the main driving mode, and establishes a dynamic prediction model for oil and gas field injection and production based on the linear dynamic system (LDS). The introduction of hidden variables in the model better characterizes the injection-production relationship in actual production, and can make accurate predictions on monthly production. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of the method for dynamic prediction of oil and gas field injection and production output based on linear dynamic system of the present invention;

[0024] Figure 2 The five-point method is used in the embodiment of the present invention to measure the injection well to the production well q in the area well pattern. 1 Schematic diagram of the control volume;

[0025] Figure 3This is a graph showing the monthly injection volume and monthly production change of a block in an embodiment of the present invention;

[0026] Figure 4 This is a comparison chart of the changes in ten predicted values ​​and actual values ​​of a block dynamic system (LDS) model of an embodiment of the present invention: (a) all time periods, (b) test set time

[0027] Figure 5 This is a comparison chart of the predicted average value and actual value of a certain block dynamic system (LDS) model in an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The present invention will be further described in detail below in conjunction with the embodiments, but the embodiments of the present invention are not limited thereto.

[0029] Figure 1 The flow of the method for dynamic prediction of injection and production output of oil and gas fields based on a linear dynamic system according to the present invention is shown.

[0030] The LDS prediction model is studied in a block of an oil and gas field in a certain region. From June 1992 to December 2009, there were 13 injection wells and 11 production wells in the block. After preprocessing the monthly production data, 210 groups of data with effective block monthly total injection volume and block monthly total production volume were screened out. A method for dynamic prediction of injection and production output of oil and gas fields based on a linear dynamic system provided by the present invention was used, which includes the following steps:

[0031] Step S1: Based on the control material balance equation of the entire reservoir of the water-driven oil and gas field, a linear dynamic system (LDS) production prediction model is established;

[0032] In the production process of water-driven oil and gas fields, the controlling material balance equation of the entire reservoir is:

[0033]

[0034] Among them, c t is the total compressibility, MPa -1 ; V p is the pore volume of the reservoir, m 3 ; is the average rate of change of reservoir pressure, MPa / t; i(t) and q(t) represent the total injection rate and production rate at time t, respectively, m 3 / t.

[0035] Assuming that reservoir pressure is a general function of time and location, The rate of change is:

[0036]

[0037] in, is a vector representing a specific geological location in the reservoir.

[0038] Assume the reservoir volume Then the controlling material balance equation of the entire reservoir will be converted to:

[0039] V′(t)=i(t)-q(t)

[0040] Among them, V′(t) is the rate of change of the control volume, which is dimensionless. The control volume refers to the volume of the reservoir space between a specific injection well and a specific production well. The fluid will flow from the injection well to the production well through this reservoir space. The fluid in the injection well is used to drive oil and gas production. The definition of control volume is introduced to characterize the connectivity between wells, so the production process in the reservoir can be better described and the production capacity can be predicted.

[0041] The reservoir control material balance equation is established for the reservoir model with I injection wells and J production wells. where i i (t) represents the injection rate of the i-th injection well, where q j (t) represents the production rate of the jth production well, and V ij represents the control volume from injection well i to production well j, V′ ij (t) represents the rate of change of the control volume from injection well i to production well j, and the material balance equation of injection well i and production well j after transformation is obtained:

[0042] V′ ij (t) = i t (t)-q j (t)

[0043] Among them, V′ ij It is a function of time and location, reflecting the dynamic changes in reservoir volume at different geological locations.

[0044] Assume that for a particular production well j, its production rate q j Affected by all injection wells, the formula is used It represents the control volume change rate of all i injection wells for the specified production well j. For the specified production well j, the contribution rate of each injection well i to its production is different, so the idea of ​​weighted contribution rate is introduced. Generally speaking, the farther the injection well is from the production well, the smaller its contribution rate to the production, so the material balance equation of injection well i and production well j becomes:

[0045]

[0046] Among them, α and β are coefficient column vectors, and each number in the vector represents the weight of the contribution rate of each injection well to a specific production well.

[0047] by Figure 2 Production wells q in the area well pattern of the five-point method 1 For example, it is affected by the injection well i 1 ,…,i 5 The direct impact of injection well i is that due to the different distances from each injection well, each injection well contributes differently to the production well. From the size of the control volume (arrow in the figure), we can get: injection well i 1 ,i 2 ,i 3 For production wells 1 The contribution rate of injection well i is greater than that of injection well i 4 ,i 5 The contribution rate of production well q 1 The material balance equation is:

[0048]

[0049] The injection rate is used as the system input, the production rate is used as the system output, and the control volume change rate is used as the hidden state change. A reservoir production prediction model is established based on the linear dynamic system (LDS). The state update of the control volume change rate is not only related to the previous control volume change rate, but also affected by the system input (i.e., the injection rate). represents the control volume change rate of production well j at time t+Δt, then:

[0050]

[0051] Among them, ε(t) is used to update Gaussian noise.

[0052] Discretize the time step of the above formula to get:

[0053]

[0054] Here, n is the discrete time step.

[0055] In order to simplify the calculation process, we assume that the f function here is a linear recursive function, that is,

[0056]

[0057] in, The coefficient matrix of The coefficient matrix of .

[0058] Similarly, the material balance equation in the above formula is discretized to obtain the observation equation of production well j:

[0059]

[0060] Where γ(n) is Gaussian noise with known production rate.

[0061] Combining the above two equations, we can get the linear dynamic system model of production well j:

[0062]

[0063]

[0064] To simplify the representation, let the vector z n represents the rate of change of the control volume, Indicates z n The initial value of Let vector u n represents the system input, i.e., the injection rate Let the scalar y n represents the system output, i.e., the production rate q of production well j j (n), the resulting system equation consists of three parts:

[0065] The hidden state equation is:

[0066] z n+1 =Az n +Bu n +w,w~N(0,Q)

[0067] The observation equation is:

[0068] x n =Hz n +Cu n +v,v~N(0,R)

[0069] The initial state of the model is:

[0070]

[0071] Where s is the noise coefficient of the initial state variable, dimensionless; w is the system noise coefficient, dimensionless; v is the observation noise coefficient, dimensionless; Q, R, V 0 are the covariance matrix coefficients of w, v, and s respectively, and are dimensionless. Step S2: using the EM method to estimate the model parameters in the linear dynamic system LDS production prediction model;

[0072] The parameters are iteratively updated in two steps, and all calculation processes are implemented through Python programming.

[0073] The first step: After manually initializing the model parameters θ, the predicted value of the data is obtained. This process is divided into two steps.

[0074] (1) Kalman filtering process, which is a forward recursive process, the calculation formula is as follows:

[0075]

[0076]

[0077]

[0078]

[0079]

[0080] (2) Kalman smoothing process, which is a backward recursive process, and the calculation formula is as follows:

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] The second step is to use the predicted values ​​of the obtained data to estimate the model parameters θ in turn, which is mainly divided into two steps.

[0089] (1) Step E: From the assumption, we know that the state variable z n With the observed variable x n The joint distribution function of is:

[0090]

[0091] Among them, p(z 1 ), p(z n |z n-1 ) and p(x n |z n ) all satisfy the Gaussian distribution, and have:

[0092]

[0093]

[0094]

[0095] Calculate the Q(θ,θ of the above three equations respectively old )=E Z [log p(X,Z|θ)] gives:

[0096]

[0097]

[0098]

[0099] (2) M steps, in order to find the maximum value, we need to 1 , Q 2 , Q 3 Derivatives are taken with respect to the parameters and their derivatives are set to zero to obtain:

[0100] Model parameter u 0 ,V 0 The estimated formula is:

[0101] u 0 =E[z 1 ],

[0102] The estimated values ​​of model parameters A and B require the following simultaneous equations:

[0103]

[0104]

[0105] The estimated values ​​of model parameters H and C require the following simultaneous equations:

[0106]

[0107]

[0108] The estimation formula of model parameter Q is:

[0109]

[0110] The estimation formula of model parameter R is:

[0111]

[0112] Among them: the values ​​​​of A, B and H, C are the model parameter values ​​​​after update.

[0113] There are three important expected values ​​in the process of updating model parameters, which can be obtained based on the calculation results of Kalman filtering + smoothing process in the first step. The calculation formula includes:

[0114]

[0115]

[0116]

[0117] The model parameters to be solved are θ = {A, B, H, C, Q, R, V 0 ,u 0}, where the initialization parameters are given artificially, and then the EM method is used to update the model parameters.

[0118] Step S3: organize and divide the dynamic data, divide the data set into training set and test set according to a certain ratio;

[0119] Figure 3 The figure is a graph of the monthly injection volume and monthly production data of the block changing over time. According to the ratio of training set: test set = 7:3, the total monthly injection volume and total monthly production of the block in the first 147 months are set as the LDS model training set, and the injection volume and production data in the last 63 months are used as the prediction set.

[0120] Step S4: Initialization of model parameters and parameter calculation, integration of prediction results and calculation of relative errors;

[0121] The model parameters are initialized using random normal distribution, and the total monthly injection volume of the block is used as the input of the LDS model system. The maximum number of iterations is set to 500. In order to prevent overfitting of the model, the error ε is set to 0.0001. After a total of 10 iterations of the LDS model training, the relationship between the LDS model system output and the actual production data of the block is obtained, as shown in the figure. Figure 4 shown.

[0122] The relative error between the actual production and the predicted production of the block after 10 iterations is obtained. It can be seen from Table 1 that the prediction results of the model are stable to a certain extent. The relative error of 80% of the models is stable at about 6%. The final monthly production prediction value is obtained by averaging the 10 prediction results, as shown in Figure 5 As shown, the relative errors of the training set and the test set were 1.55% and 5.49% respectively. The prediction accuracy is high and sufficient to meet production and research needs.

[0123] Table 1 MAPE statistics of ten predicted values ​​and actual values ​​of block LDS model

[0124]

[0125] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention in any form. Any simple modification or equivalent change made to the above embodiment based on the technology and method of the present invention shall fall within the protection scope of the present invention.

Claims

1. A dynamic prediction method for oil and gas field injection and production based on linear dynamic system, It is characterized in that The following steps are involved: Step S1: Based on the control material balance equation of the entire reservoir of the water-driven oil and gas field, a linear dynamic system LDS production prediction model is established; Step S2: using the expectation maximization (EM) method to estimate the model parameters in the linear dynamic system LDS production prediction model; Step S3: organize and divide the dynamic data, divide the data set into training set and test set according to a certain ratio; Step S4: initialization of the model parameters and parameter calculation, integration of prediction results and calculation of relative errors; in step S1, during the exploitation of the water-driven oil and gas field, the controlling material balance equation of the entire reservoir is: in, is the total compressibility, MPa -1 ; is the pore volume of the reservoir, m 3 ; is the average rate of change of reservoir pressure, MPa / t; and Respectively indicate time Total injection rate and production rate at m 3 / t; In step S1, the linear dynamic system LDS production prediction model includes three parts: Hidden state equation: Observation equation: The initial state of the model: in, is the noise coefficient of the initial state variable, dimensionless; is the system noise factor, dimensionless; To observe the noise factor, it is dimensionless; , , They are ， ， The covariance matrix coefficients of , dimensionless.

2. The method for dynamic prediction of oil and gas field injection and production output based on a linear dynamic system according to claim 1, Features: In step S2, the model parameters are iteratively updated in two steps. The first step is to obtain the predicted values ​​of the data after manually initializing the model parameters; the second step is to estimate the model parameters in reverse using the predicted values ​​of the obtained data; all calculation processes are implemented through Python programming.

3. The method for dynamic prediction of oil and gas field injection and production output based on linear dynamic system according to claim 2, Features: In step S3, the ratio of the training set to the test set is 7:

3.

4. The method for dynamic prediction of oil and gas field injection and production output based on a linear dynamic system according to claim 2, Features: In step S4, the relative errors between the training set and the test set are less than 5% and 10% respectively, which meets the accuracy requirement; the final monthly output forecast value is equal to the average value of the 10 forecast results.

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