CN109543828B - Water absorption profile prediction method based on small sample condition - Google Patents
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Abstract
The invention discloses a water absorption profile prediction method based on a small sample condition, which is used for collecting multi-source data of an oil field block to be analyzed; performing inter-well connectivity analysis and grey correlation analysis, determining static and dynamic factors influencing a water absorption profile, and performing normalization processing to form a standard water absorption profile small sample library; establishing a cost function integrating multiple tasks by taking the small layers as a machine learning unit, and obtaining a generalized model adapting to the water absorption prediction of each small layer by taking gradient descent as a learning algorithm; and (3) further carrying out parameter fine adjustment and personalized learning by depending on limited water absorption profile data of the water injection well, establishing a water absorption capacity prediction model suitable for the water absorption splitting rule of the water injection well, and realizing continuous dynamic prediction of the water absorption profile based on the model. The method is based on the machine learning theoretical basis under the condition of small samples, realizes accurate splitting of water injection quantity and prediction of water absorption profile, has important significance for recognizing underground residual oil distribution, and is the basis for realizing layered production allocation and injection allocation of intelligent oil fields.
Description
Technical Field
The invention belongs to the field of oil and gas field development, and particularly relates to a water absorption profile prediction method based on a small sample condition.
Background
Water injection is the main technology of oilfield development in China, and the continuous improvement of the water drive recovery ratio in the later period of high water content and the ultra-high water content is still one of the main attack directions for improving the recovery ratio, and although the difficulty is very high, the adaptability is very wide. However, most of the Chinese oil fields are continental-phase oil fields, the sedimentary rhythm is complex, the reservoir heterogeneity is severe, the contradiction between layers and in layers is particularly prominent in the development process, and further the tongue-in phenomenon of the injected water in the plane direction of the production well and the protrusion phenomenon of the injected water in the longitudinal direction of the high permeable layer are caused, so that the injected water is ineffective in circulation to influence the water injection effect.
For a long time, the prediction of the water injection well water absorption profile is an important basis for calculating the water injection well stratified water injection amount and the accumulated water absorption amount, and the splitting of the small-layer water absorption amount of each water injection well is the most important link for researching the flooding condition and the oil displacement efficiency of an injection and production well group in the middle and later periods of the development of a water injection oil field. The calculation of the water absorption capacity of the small layer of the water injection well mainly comprises a seepage mechanics calculation method, a splitting component method, a water absorption profile interpolation method and a numerical simulation method. The method does not fully consider the influence and the constraint of the connectivity, the pressure difference and the material conservation of the reservoir, and the calculation result of the method cannot accurately reflect the actual water injection condition of each interval of the oil reservoir. The water absorption profile test of the mine field is that the difference of the radioactive intensity of each small layer is obtained by injecting the isotope into the well under the condition of water injection, namely the water absorption capacity. The water absorption profile obtained by the method is most suitable for the actual water absorption condition of a small layer, but the well shut-in and production halt are needed for measurement, the test period is long, the cost is high, the water absorption profile data measured on site are few and discontinuous, even a plurality of water injection wells have no water absorption profile data, and great difficulty is brought to water injection splitting.
How to fully utilize the existing water absorption profile data and realize the continuous prediction of the water absorption profile at the time point of the non-water absorption profile becomes a difficult problem to be solved urgently. The water absorption profile prediction method based on data mining is the most effective method for solving the splitting problem of water injection amount by deeply mining the rules and relations hidden in the existing water absorption profile data and establishing a correlation relation model of a water absorption profile and an injection and production system so as to realize inversion and prediction of the water absorption profile. The methods mainly comprise two main categories: the method comprises a water absorption section prediction method based on an adaptive fuzzy neural network and a water absorption section prediction method based on a support vector. The existing method mainly has the following three problems: 1. the dynamic change of the water absorption profile data cannot be accurately reflected, and the considered dynamic influence factors are few and not comprehensive; 2. the research focuses on the prediction of the water absorption profile of the water injection well with a small amount of water absorption profile data, and the prediction of the water absorption profile of the water injection well without the water absorption profile data is rarely researched; 3. the machine learning method relying on big data training is used for solving the problem of small sample learning, and the prediction accuracy of the water absorption profile is low.
Disclosure of Invention
In view of the above, the present invention provides a water absorption profile prediction method based on a small sample condition, which aims at the problems in the prior art.
In order to solve the technical problem, the invention discloses a water absorption profile prediction method based on a small sample condition, which specifically comprises the following steps:
the method comprises the following steps: collecting multi-source data aiming at an oil field block to be analyzed and researched, and constructing an original data set;
step two: determining static parameters and dynamic parameters influencing the water absorption capacity of the small layer according to the inter-well connectivity analysis result and the grey correlation analysis, thereby forming the characteristic dimension of the water absorption profile small sample data set and realizing the construction of a primary water absorption profile small sample database;
step three: analyzing and fusing the primary small sample database by small layers of data, unifying the characteristic dimension of each small layer, carrying out normalization processing on the data, realizing the construction of the standard water absorption profile small sample database, and dividing the sample set corresponding to each small layer into a training set, a verification set and a test set according to the ratio of 6:2: 2;
step four: building an initial structure of a neural network, and randomly initializing a weight coefficient;
step five: establishing a cost function of machine learning layer by layer;
step six: learning and training of each small-layer neural network model are completed on a training data set, repeated verification and evaluation are carried out on a verification set based on a grid search method, and the most appropriate number of hidden layers and the number of neuron nodes are determined;
step seven: establishing an integrated multi-task optimized objective function on the test set by utilizing the neural network models of all the small layers trained in the step six, introducing a gradient descent optimization algorithm, and performing generalized learning on the water absorption prediction model of the small layers to obtain a generalized neural network model suitable for the water absorption rule of all the small layers;
step eight: repeating the fifth step to the seventh step, and continuing the learning and parameter updating of the neural network;
step nine: based on a generalization model, based on a small amount of water absorption profile data of the water injection well, parameter fine tuning and personalized learning of a neural network model are carried out, a water absorption prediction model suitable for each small layer is obtained, and a water absorption profile prediction model suitable for the water injection well is further obtained.
Optionally, the data collected in step one comprises: porosity, permeability, thickness, extremely poor permeability, coefficient of variation, discontinuous water absorption profile of a single well and corresponding relation of the discontinuous water absorption profile and a small layer, water injection amount, injection pressure, liquid production amount, water content, working fluid level height, commingled production, commingled injection information, perforation layer position, well completion mode and well spacing of an oil-water well.
Optionally, the inter-well connectivity analysis in the second step specifically includes:
there are many injection wells and production wells in the oil reservoir, and when the liquid production capacity of every production well was aroused by many injection wells, according to the stack principle combination material conservation relation, it was:
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
represents the predicted production, i, of the model for the producing well, jijIndicates the injection amount of the water injection well i, qojA constant term representing injection-production unbalance, 0 when injection-production is balanced,λij,τijrespectively representing the communication coefficient and the time lag constant, tau, of the water injection well i and the production well jpReflecting the extent of influence of the initial production on the production well production, pwfjRepresenting the bottom hole pressure, v, of the producing well jjA weight representing the effect of bottom hole pressure fluctuations on production;
parameters to be determined in a capacitance model
Can be obtained by inversion of historical injection and production data, and thus the inversion and fitting objective function is established as follows:
in the formula, qj(t) represents the actual production of production well j;
solving the minimum value of the objective function of the formula (2) by a gradient descent algorithm, wherein the parameter iteration process is as follows:
in the formula, xk+1,xkRespectively representing the parameter values of k +1 and k in the iterative step, eta represents the step length,
representing the gradient of the objective function.
At the moment, the objective function takes the parameter to be optimized corresponding to the minimum value
Namely the finally obtained parameters, and further the communication coefficient lambda of the production well j and the surrounding water injection well is obtainedij(ii) a And replacing the researched target production well, and repeating the connectivity analysis process to obtain the connectivity between each production well and the surrounding water injection wells, in other words, the connectivity between the water injection wells and the surrounding production wells.
Optionally, the grey correlation analysis in step two is as follows:
a. and constructing a data analysis matrix according to the connectivity analysis result and the collected well area data:
in the formula, m represents the number of samples, the value of the number is the sum of the products of each small layer number and the monitoring times of the water absorption profile, n represents the preliminarily determined water absorption profile influence factor, the value is (number of communicated oil wells +1) × (static parameters + dynamic parameters), wherein 1 represents the current water injection well, the static parameters comprise porosity, permeability and effective thickness, and the dynamic parameters comprise yield or injection amount and dynamic liquid level height;
b. determining reference data columns
The reference data column here, i.e. the water absorption of the sublayer, is recorded as:
X'0＝(x'0(1),x'0(2),…,x'0(m)) (5)
c. dimensionless of data
Carrying out non-dimensionalization on the data by an averaging method to obtain a non-dimensionalized data matrix as follows:
d. calculating the correlation degree between each influence factor and the water absorption capacity of the small layer
Calculating the association degree r between the water absorption capacity of the small layer and the ith influence factor0iThe formula is as follows:
wherein the content of the first and second substances,
where ρ represents a resolution coefficient, usually 0.5;
and determining main factors influencing the water absorption profile according to the correlation degree among the parameters.
Optionally, the step three is specifically:
normalization is performed by a dispersion normalization method, and the formula is as follows:
xstd＝(x-xmin)/(x-xmax) (8)
wherein x represents the original data in the data sample and has the unit of m3/d，xminAnd xmaxRespectively representing the maximum and minimum values, x, of the corresponding datastdNormalized values for the data.
Optionally, the step four specifically includes:
and (3) taking the number of the main influence factors screened out in the step three as the input of the neural network, taking the number of the neurons as the characteristic dimension, expressing the water absorption capacity of the small layer by the output layer, setting the number of the neurons as 1, setting the initial hidden layer number as 1, and determining the initial number of the neurons by the following empirical formula (9):
in the formula, NHNRepresenting the number of hidden layer neurons, NIIndicates the number of input neurons, NORepresenting the number of output neurons;
and the weight coefficient to the neural network is in the interval [ -init，init]A random initialization is performed and the random initialization is performed,initformula (10) is calculated from the following formula:
in the formula (I), the compound is shown in the specification,initthe upper limit of the value initialized for the weight coefficient is set as the corresponding lower limitinit，LinAnd LoutRespectively representing the number of nodes of the front and rear connection layers of the unit layer.
Optionally, the step five specifically includes:
the small layers are taken as a unit for machine learning, so that the water absorption prediction of each small layer is taken as a learning task, and respective cost functions are established; each small-layer cost function includes two terms: the error square sum of the actual water absorption of the small layer and the predicted value of the neural network; a regularization term with respect to the weight coefficients;
taking the k-th learning task as an example, the specific equation of the machine learning cost function is as follows:
in the formula, JkAs an objective function for the k-th sublayer,
showing the water absorption capacity of the kth sublayer,
shows the predicted value of the water absorption of the k small layer,
representing weight coefficients of the neural network, λ representing a regularization parameter, NkAnd M represents the number of samples, and M represents the number of weight coefficients to be optimized in the neural network.
Optionally, the step six specifically includes:
aiming at each learning task, updating the weight coefficient of the neural network by adopting a gradient descent algorithm, taking the kth learning task as an example, and updating the parameters as follows:
in the formula, thetak' is the updated weight coefficient vector, theta is the initial weight coefficient vector, alpha is the learning rate, can be given artificially,
representing the gradient of the objective function.
Optionally, the step seven is specifically:
in order to obtain a generalization model adapting to water absorption profile prediction, an integrated multi-task objective function is established on the basis of a neural network model after initial learning, and the form of the integrated multi-task objective function is as follows:
and (3) carrying out optimization solution on the objective function of the formula (13) by using a gradient descent algorithm to obtain the weight of the generalized model, wherein the parameter updating process comprises the following steps:
wherein θ is a vector of the weight coefficients of the generalized model,
gradient representing the objective function, NlayerRepresents the number of small layers, and β is the learning rate.
Optionally, the step nine specifically is:
(1) generalized model-based objective function establishment
The objective function is similar to the objective function of a single learning task established in the step five, but the difference is that the predicted value in the objective function is the generalized model obtained in the step seven, and the specific equation form is as follows:
wherein m represents the number of samples of the target small layer, hθ(xi) Representing the predicted value of the generalized neural network model, and theta represents the weight coefficient of the generalized neural network model;
(2) personalized learning based on small sample data
Based on the limited water absorption profile data of the small layer, the parameters of the neural network model are quickly adjusted, and the parameter updating process is as follows:
in the formula, thetai+1,θiRespectively representing model parameters in the i +1 th and i th iteration steps,
expressing the gradient of the objective function, and gamma is the learning rate;
(3) calculation of water absorption profile of water injection well
Replacing the target small layer, repeating the fine adjustment of the parameters to obtain an individual water absorption prediction model suitable for each small layer of the water injection well, and calculating the percentage d of the water absorption of the small layer to the injection amount of the water injection well according to a formula (17)kThe relative water absorption is obtained, and a water absorption profile of the water injection well is drawn according to the value;
in the formula (d)kIs the relative water absorption of each k th small layer of the water injection well, qkThe water absorption amount of the kth small layer is shown, and K is the number of perforation layers of the water injection well.
Compared with the prior art, the invention can obtain the following technical effects:
1) the method is based on the machine learning theoretical basis under the condition of small samples, realizes accurate splitting of water injection quantity and prediction of water absorption profile, has important significance for recognizing underground residual oil distribution, and is the basis for realizing layered production allocation and injection allocation of intelligent oil fields.
2) Determining main factors influencing a water absorption profile by utilizing an interwell connectivity analysis method and a gray level correlation analysis method; the limited water absorption profile data is utilized, the accurate inversion and prediction of the water absorption profile of the water injection well are realized by means of a small data learning algorithm, and the accuracy of water injection splitting is improved;
3) through the established water absorption profile prediction model, the water absorption profile prediction of each production time period of the water injection well is realized, and the current situations of insufficient profile data on site monitoring and inaccurate water injection splitting are made up.
Of course, it is not necessary for any one product in which the invention is practiced to achieve all of the above-described technical effects simultaneously.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic diagram of a well pattern model of a block to be studied;
FIG. 2 is a technical roadmap for the study protocol of the present invention;
FIG. 3 is a plot of well-to-well connectivity for a block;
FIG. 4 is a structure of a single hidden layer artificial neural network model;
FIG. 5 is a graph showing the dynamic change of the predicted water absorption capacity of the sublayer 1 with time according to the present invention;
FIG. 6 is a graph showing the dynamic change of the predicted water absorption capacity of the sublayer 2 with time according to the present invention;
FIG. 7 is a graph showing the dynamic change of the predicted water absorption capacity of the sublayer (3) with time according to the present invention;
FIG. 8 is a graph showing the dynamic change of the predicted water absorption capacity of the sublayer 4 with time according to the present invention;
FIG. 9 is a comparison of a predicted water absorption profile and a measured water absorption profile for a water injection well I1 at t 12 months according to the present invention;
FIG. 10 is a comparison of a predicted water absorption profile and a measured water absorption profile for a water injection well I1 at t 24 months according to the present invention;
fig. 11 is a comparison of the predicted water absorption profile and the measured water absorption profile of a water injection well I1 at t-30 months according to the present invention.
Detailed Description
The following embodiments are described in detail with reference to the accompanying drawings, so that how to implement the technical features of the present invention to solve the technical problems and achieve the technical effects can be fully understood and implemented.
A block to be investigated has a closed fault as shown in fig. 1. The average effective thickness of the stratum is 4m, and the permeability is kx＝ky＝60md，kz＝0.01kxPorosity 0.359, grid length and width 25m, total 30 × 30 × 5-4500And (4) grid. The block well group has five water injection wells and four production wells, oil-water two-phase flow exists in an oil reservoir, and injection and production dynamic data are oilfield field data.
For the above example, the method for predicting the water absorption profile based on the small sample condition is combined, as shown in fig. 2, and specifically includes the following steps:
the method comprises the following steps: collecting multi-source data aiming at an oil field block to be analyzed and researched, and constructing an original data set;
the data collected mainly includes: geological interpretation data (data such as porosity, permeability, thickness, permeability range, coefficient of variation and the like), water absorption profile data (data such as a single-well discontinuous water absorption profile and a corresponding relation between the single-well discontinuous water absorption profile and a small layer), production dynamic data (data such as water injection amount, injection pressure, liquid production amount, water content and dynamic liquid level height) and production measure information (data such as commingled production, combined injection information, perforation layer position, well completion mode, well spacing of an oil-water well and the like).
Step two: determining static parameters and dynamic parameters influencing the water absorption capacity of the small layer according to the inter-well connectivity analysis result and the grey correlation analysis, thereby forming the characteristic dimension of the water absorption profile small sample data set and realizing the construction of a primary water absorption profile small sample database;
the collected historical injection and production data are used for judging the communication conditions of all the production wells and the surrounding water injection wells in the research area based on a capacitance model (CRM), and the communication conditions of the water injection wells and the surrounding production wells are counted by taking the water injection wells as a research target, wherein the communication conditions are shown in figure 3. And further based on a grey correlation analysis method, calculating the correlation degree between the water absorption capacity of the small layer and the static and dynamic parameters of the surrounding production wells, eliminating invalid parameters in the original data set, determining main factors influencing a water absorption profile, and constructing a small sample data set of the primary water absorption profile by combining the water absorption capacity of the small layer.
The main factors identified here include: relevant parameters of the water injection well, such as porosity, permeability, injection pressure and other data; and relevant parameters of the oil well, such as porosity, permeability, liquid production amount, water content and the like. In order to accurately represent main influence factors of the water absorption profile, the existing data needs to be fully utilized to carry out inter-well connectivity analysis and grey correlation analysis, so as to determine main static parameters and dynamic parameters influencing the water absorption profile.
(1) Inter-well connectivity analysis
There are many injection wells and production wells in the oil reservoir, and when the liquid production capacity of every production well was aroused by many injection wells, according to the stack principle combination material conservation relation, it was:
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
represents the predicted production, i, of the model for the producing well, jijIndicates the injection amount of the water injection well i, qojConstant term representing injection-production unbalance, 0, lambda when injection-production is balancedij,τijRespectively representing the communication coefficient and the time lag constant, tau, of the water injection well i and the production well jpReflecting the extent of influence of the initial production on the production well production, pwfjRepresenting the bottom hole pressure, v, of the producing well jjA weight representing the effect of bottom hole pressure fluctuations on production;
the right end of formula (1) contains four parts: the first part represents a constant term of injection-production unbalance; the second part is the influence of the initial value of the initial liquid production amount; the third part is the influence of the initial value of the liquid production amount; the fourth part is the effect of pressure fluctuations downhole in the production well on production.
Parameters to be determined in a capacitance model
Can be obtained by inversion based on historical injection and production data, thus establishing an inversion and fitting objective function as follows:
in the formula, qj(t) represents the actual production of production well j;
solving the minimum value of the objective function of the formula (2) by a gradient descent algorithm, wherein the parameter iteration process is as follows:
in the formula, xk+1,xkRespectively representing the parameter values of k +1 and k in the iterative step, eta represents the step length,
representing the gradient of the objective function.
At the moment, the objective function takes the parameter to be optimized corresponding to the minimum value
Namely the finally obtained parameters, and further the communication coefficient lambda of the production well j and the surrounding water injection well is obtainedij(ii) a And replacing the researched target production well, and repeating the connectivity analysis process to obtain the connectivity between each production well and the surrounding water injection wells, in other words, the connectivity between the water injection wells and the surrounding production wells.
(2) The grey correlation analysis is as follows:
a. and constructing a data analysis matrix according to the connectivity analysis result and the collected well area data:
in the formula, m represents the number of samples, the value of the number is the sum of the products of the number of small layers and the monitoring times of the water absorption profile, n represents the influence factor of the water absorption profile determined preliminarily, the value is (number of communicated oil wells +1) × (static parameters + dynamic parameters), wherein 1 represents the current water injection well, the static parameters comprise porosity, permeability, effective thickness and the like, and the dynamic parameters comprise yield or injection amount, dynamic liquid level height and the like;
b. determining reference data columns
The reference data column here, i.e. the water absorption of the sublayer, is recorded as:
X'0＝(x'0(1),x'0(2),…,x'0(m)) (5)
c. dimensionless of data
Due to the different physical meanings of the factors in the system, the data dimensions are not necessarily the same, which is inconvenient for comparison or makes it difficult to obtain correct conclusions during comparison. Carrying out non-dimensionalization on the data by an averaging method to obtain a non-dimensionalized data matrix as follows:
d. calculating the correlation degree between each influence factor and the water absorption capacity of the small layer
Calculating the association degree r between the water absorption capacity of the small layer and the ith influence factor0iThe formula is as follows:
wherein the content of the first and second substances,
where ρ represents a resolution coefficient, usually 0.5;
and determining main factors influencing the water absorption profile according to the correlation degree among the parameters.
Step three: analyzing and fusing the primary small sample database by small layers of data, unifying the characteristic dimension of each small layer, carrying out normalization processing on the data, realizing the construction of the standard water absorption profile small sample database, and dividing the sample set corresponding to each small layer into a training set, a verification set and a test set according to the ratio of 6:2: 2;
normalization is performed by a dispersion normalization method, and the formula is as follows:
xstd＝(x-xmin)/(x-xmax) (8)
wherein x represents the original data in the data sample and has the unit of m3/d，xminAnd xmaxRespectively representing the maximum and minimum values, x, of the corresponding datastdNormalized values for the data.
Step four: building an initial structure of a neural network, and randomly initializing a weight coefficient;
and (4) taking the number of the main influence factors screened out in the step three as the input of the neural network, wherein the number of the neurons is the number of the influence factors of the water absorption capacity of the small layer, namely the dimensionality of the characteristic parameters. The output layer represents the water absorption of the sublayer, the number of neurons is 1, the initial number of hidden layers is set to 1, and the initial number of neurons is determined by the following empirical formula (9): a single layer neural network structure is shown in figure 4,
in the formula, NHNRepresenting the number of hidden layer neurons, NIIndicates the number of input neurons, NORepresenting the number of output neurons;
and the weight coefficient to the neural network is in the interval [ -init，init]A random initialization is performed and the random initialization is performed,initformula (10) is calculated from the following formula:
in the formula (I), the compound is shown in the specification,initthe upper limit of the value initialized for the weight coefficient is set as the corresponding lower limitinit，LinAnd LoutRespectively representing the number of nodes of the front and rear connection layers of the unit layer.
Step five: establishing a cost function of machine learning layer by layer;
the small layers are taken as a unit for machine learning, so that the water absorption prediction of each small layer is taken as a learning task, and respective cost functions are established; each small-layer cost function includes two terms: the error square sum of the actual water absorption of the small layer and the predicted value of the neural network; a regularization term with respect to the weight coefficients;
for this block, 4 layers are all jetted out for 5 water injection wells, and 20 cost functions are required to be established. Taking the k-th learning task as an example, the specific equation of the machine learning cost function is as follows:
in the formula, JkAs an objective function for the k-th sublayer,
showing the water absorption capacity of the kth sublayer,
representing the predicted values for the k small layer input,
represents the weight coefficient of the neural network, and λ represents the regularization parameter, here, the value is 0.001, NkAnd M represents the number of samples, and M represents the number of weight coefficients to be optimized in the neural network.
Step six: learning and training of each small-layer neural network model are completed on a training data set, repeated verification and evaluation are carried out on a verification set based on a grid search method, and the most appropriate number of hidden layers and the number of neuron nodes are determined;
and respectively optimizing and solving the neural network weight coefficient corresponding to the minimum value of the cost function in the fifth step on the training data set by using a gradient descent optimization algorithm, and determining the optimal number of hidden layers and the number of neuron nodes thereof on the verification set based on grid search to complete the initial learning process of the neural network.
Aiming at each learning task, updating the weight coefficient of the neural network by adopting a gradient descent algorithm, taking the kth learning task as an example, and updating the parameters as follows:
in the formula, thetak' is the updated weight coefficient vector, theta is the initial weight coefficient vector, alpha is the learning rate, can be given artificially,
representing the gradient of the objective function.
In order to determine the optimal neural network structure, the hyper-parameters of the neural network need to be adjusted. By means of a combination mode of exhausting the hidden layer number and the neuron node number, all possibilities are traversed by a grid search method, verification and evaluation are repeated on a verification data set, and then the optimal parameter combination, namely the appropriate hidden layer number and the neuron node number, is determined.
Finally, the single hidden layer and the 15 nodes are determined as the optimal parameter combination.
Step seven: establishing an integrated multi-task optimized objective function on the test set by utilizing the neural network models of all the small layers trained in the step six, introducing a gradient descent optimization algorithm, and performing generalized learning on the water absorption prediction model of the small layers to obtain a generalized neural network model suitable for the water absorption rule of all the small layers;
in order to obtain a generalization model adapting to water absorption profile prediction, an integrated multi-task objective function is established on the basis of a neural network model after initial learning, and the form of the integrated multi-task objective function is as follows:
in the formula, Nlayer＝20。
And (3) carrying out optimization solution on the objective function of the formula (13) by using a gradient descent algorithm to obtain the weight of the generalized model, wherein the parameter updating process comprises the following steps:
wherein θ is a vector of the weight coefficients of the generalized model,
gradient representing the objective function, NlayerRepresents the number of small layers, and β is the learning rate, here, 0.05.
Step eight: repeating the fifth step to the seventh step, and continuing the learning and parameter updating of the neural network;
step nine: based on a generalization model, based on a small amount of water absorption profile data of the water injection well, parameter fine tuning and personalized learning of a neural network model are carried out, a water absorption prediction model suitable for each small layer is obtained, and a water absorption profile prediction model suitable for the water injection well is further obtained.
And D, directly predicting the water absorption capacity of the small layer by using the water absorption profile generalization model obtained in the step seven, wherein the precision is very low. In order to obtain a model adaptive to the water absorption prediction of a target stratum on the basis of the generalized model, the trained generalized model needs to be updated and fine-tuned again by using the limited water absorption profile data of the water injection well to be analyzed, so as to obtain a water absorption prediction model adaptive to each stratum. According to the prediction model, the continuous prediction of the water absorption change of each small layer can be realized, and the accurate splitting of the water absorption of the well water injection well is further realized.
Parameter fine adjustment is also a machine learning process, and a better basic generalized model which can be widely suitable for predicting the water absorption capacity of each small layer is provided, so that the water absorption capacity prediction model suitable for the target small layer can be obtained only by needing a small amount of sample data of the target small layer and only needing parameter updating for several times.
(1) Generalized model-based objective function establishment
The objective function is similar to the objective function of a single learning task established in the step five, but the difference is that the predicted value in the objective function is the generalized model obtained in the step seven, and the specific equation form is as follows:
wherein m represents the number of samples of the target small layer, hθ(xi) Representing the predicted value of the generalized neural network model, and theta represents the generalizedWeight coefficients of the neural network model are quantized;
(2) personalized learning based on small sample data
Based on the limited water absorption profile data of the small layer, the parameters of the neural network model are quickly adjusted, and the parameter updating process is as follows:
in the formula, thetai+1,θiRespectively representing model parameters in the i +1 th and i th iteration steps,
expressing the gradient of the objective function, and gamma is the learning rate;
(3) calculation of water absorption profile of water injection well
And replacing the target small layer, repeating the fine adjustment of the parameters to obtain an individual water absorption capacity prediction model suitable for each small layer of the water injection well, and realizing continuous dynamic prediction of the water absorption capacity of the small layer along with the change of time based on the model, as shown in the attached figures 5 to 8. Calculating the percentage d of the water absorption of the small layer to the injection of the water injection well according to the formula (17)kThat is, the relative water absorption is obtained, the water absorption profile of the water injection well is drawn according to the value, and the comparison result with the actual monitoring profile of the water injection well I1 in t-12 months, 24 months and 30 months is shown in the attached figures 9-11, and the prediction accuracy is more than 80%.
In the formula (d)kIs the relative water absorption of each k th small layer of the water injection well, qkIs the water uptake of the kth sublayer and K is the number of perforation layers of the water injection well, here equal to 4.
The invention also has the following beneficial effects:
1. determining main factors influencing a water absorption profile by utilizing an interwell connectivity analysis method and a gray level correlation analysis method;
2. the limited water absorption profile data is utilized, the accurate inversion and prediction of the water absorption profile of the water injection well are realized by means of a small data learning algorithm, and the accuracy of water injection splitting is improved;
3. the accurate splitting of the water injection amount is realized through the established water absorption profile prediction model, the method has important significance for recognizing the distribution of underground residual oil, and is the basis for realizing the layered production allocation and injection allocation of the intelligent oil field.
The invention realizes the prediction of the water absorption profile of the water injection well and the accurate splitting of the water injection quantity by mining the knowledge of limited water absorption profile data and establishing the nonlinear relation between the water absorption profile and relevant static parameters and dynamic parameters in the injection and production system based on a small data learning algorithm.
While the foregoing description shows and describes several preferred embodiments of the invention, it is to be understood, as noted above, that the invention is not limited to the forms disclosed herein, but is not to be construed as excluding other embodiments and is capable of use in various other combinations, modifications, and environments and is capable of changes within the scope of the inventive concept as expressed herein, commensurate with the above teachings, or the skill or knowledge of the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A water absorption profile prediction method based on a small sample condition is characterized by comprising the following steps:
the method comprises the following steps: collecting multi-source data aiming at an oil field block to be analyzed and researched, and constructing an original data set;
step two: determining static parameters and dynamic parameters influencing the water absorption capacity of the small layer according to the inter-well connectivity analysis result and the grey correlation analysis, thereby forming the characteristic dimension of the water absorption profile small sample data set and realizing the construction of a primary water absorption profile small sample database;
step three: analyzing and fusing the primary small sample database by small layers of data, unifying the characteristic dimension of each small layer, carrying out normalization processing on the data, realizing the construction of the standard water absorption profile small sample database, and dividing the sample set corresponding to each small layer into a training set, a verification set and a test set according to the ratio of 6:2: 2;
step four: building an initial structure of a neural network, and randomly initializing a weight coefficient;
step five: establishing a cost function of machine learning layer by layer;
step six: learning and training of each small-layer neural network model are completed on a training data set, repeated verification and evaluation are carried out on a verification set based on a grid search method, and the most appropriate number of hidden layers and the number of neuron nodes are determined;
step seven: establishing an integrated multi-task optimized objective function on the test set by utilizing the neural network models of all the small layers trained in the step six, introducing a gradient descent optimization algorithm, and performing generalized learning on the water absorption prediction model of the small layers to obtain a generalized neural network model suitable for the water absorption rule of all the small layers;
step eight: repeating the fifth step to the seventh step, and continuing the learning and parameter updating of the neural network;
step nine: based on a generalization model, based on a small amount of water absorption profile data of the water injection well, parameter fine tuning and personalized learning of a neural network model are carried out, a water absorption prediction model suitable for each small layer is obtained, and a water absorption profile prediction model suitable for the water injection well is further obtained.
2. The method of claim 1, wherein the data collected in step one comprises: porosity, permeability, thickness, extremely poor permeability, coefficient of variation, discontinuous water absorption profile of a single well and corresponding relation of the discontinuous water absorption profile and a small layer, water injection amount, injection pressure, liquid production amount, water content, working fluid level height, commingled production, commingled injection information, perforation layer position, well completion mode and well spacing of an oil-water well.
3. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 2, wherein the connectivity analysis among wells in the second step is specifically as follows:
there are many injection wells and production wells in the oil reservoir, and when the liquid production capacity of every production well was aroused by many injection wells, according to the stack principle combination material conservation relation, it was:
wherein the content of the first and second substances,
in the formula (I), the compound is shown in the specification,
represents the predicted production, i, of the model for the producing well, jijIndicates the injection amount of the water injection well i, qojConstant term representing injection-production unbalance, 0, lambda when injection-production is balancedij,τijRespectively representing the communication coefficient and the time lag constant, tau, of the water injection well i and the production well jpReflecting the extent of influence of the initial production on the production well production, pwfjRepresenting the bottom hole pressure, v, of the producing well jjA weight representing the effect of bottom hole pressure fluctuations on production; tau isjMeaning the degree of influence of bottom hole pressure fluctuation on the production well yield;
parameters to be determined in a capacitance model
Can be obtained by inversion of historical injection and production data, and thus the inversion and fitting objective function is established as follows:
in the formula, qj(t) represents the actual production of production well j;
solving the minimum value of the objective function of the formula (2) by a gradient descent algorithm, wherein the parameter iteration process is as follows:
in the formula, xk+1,xkRespectively representing the parameter values of k +1 and k in the iterative step, eta represents the step length,
a gradient representing an objective function;
at the moment, the objective function takes the parameter to be optimized corresponding to the minimum value
Namely the finally obtained parameters, and further the communication coefficient lambda of the production well j and the surrounding water injection well is obtainedij(ii) a And replacing the researched target production well, and repeating the connectivity analysis process to obtain the connectivity between each production well and the surrounding water injection wells, in other words, the connectivity between the water injection wells and the surrounding production wells.
4. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 3, wherein the grey correlation analysis in the second step is as follows:
a. and constructing a data analysis matrix according to the connectivity analysis result and the collected well area data:
in the formula, m represents the number of samples, the value of the number is the sum of the products of each small layer number and the monitoring times of the water absorption profile, n represents the preliminarily determined water absorption profile influence factor, the value is (number of communicated oil wells +1) × (static parameters + dynamic parameters), wherein 1 represents the current water injection well, the static parameters comprise porosity, permeability and effective thickness, and the dynamic parameters comprise yield or injection amount and dynamic liquid level height;
b. determining reference data columns
The reference data column here, i.e. the water absorption of the sublayer, is recorded as:
X'0＝(x'0(1),x'0(2),…,x'0(m)) (5)
c. dimensionless of data
Carrying out non-dimensionalization on the data by an averaging method to obtain a non-dimensionalized data matrix as follows:
d. calculating the correlation degree between each influence factor and the water absorption capacity of the small layer
Calculating the association degree r between the water absorption capacity of the small layer and the ith influence factor0iThe formula is as follows:
wherein the content of the first and second substances,
in the formula, rho represents a resolution coefficient and is 0.5;
and determining main factors influencing the water absorption profile according to the correlation degree among the parameters.
5. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 4, wherein the third step is specifically as follows:
normalization is performed by a dispersion normalization method, and the formula is as follows:
xstd＝(x-xmin)/(x-xmax) (8)
wherein x represents the original data in the data sample and has the unit of m3/d，xminAnd xmaxRespectively representing the maximum and minimum values, x, of the corresponding datastdNormalized values for the data.
6. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 5, wherein the step four is specifically as follows:
and (3) taking the number of the main influence factors screened out in the step three as the input of the neural network, taking the number of the neurons as the characteristic dimension, expressing the water absorption capacity of the small layer by the output layer, setting the number of the neurons as 1, setting the initial hidden layer number as 1, and determining the initial number of the neurons by the following empirical formula (9):
in the formula, NHNRepresenting the number of hidden layer neurons, NIIndicates the number of input neurons, NORepresenting the number of output neurons;
and the weight coefficient to the neural network is in the interval [ -init，init]A random initialization is performed and the random initialization is performed,initformula (10) is calculated from the following formula:
in the formula (I), the compound is shown in the specification,initthe upper limit of the value initialized for the weight coefficient is set as the corresponding lower limitinit，LinAnd LoutRespectively representing the number of nodes of the front and rear connection layers of the unit layer.
7. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 6, wherein the step five is specifically as follows:
the small layers are taken as a unit for machine learning, so that the water absorption prediction of each small layer is taken as a learning task, and respective cost functions are established; each small-layer cost function includes two terms: the error square sum of the actual water absorption of the small layer and the predicted value of the neural network; a regularization term with respect to the weight coefficients;
taking the k-th learning task as an example, the specific equation of the machine learning cost function is as follows:
in the formula, JkAs an objective function for the k-th sublayer,
showing the water absorption capacity of the kth sublayer,
shows the predicted value of the water absorption of the k small layer,
representing weight coefficients of the neural network, λ representing a regularization parameter, NkAnd M represents the number of samples, and M represents the number of weight coefficients to be optimized in the neural network.
8. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 7, wherein the sixth step is specifically as follows:
aiming at each learning task, updating the weight coefficient of the neural network by adopting a gradient descent algorithm, taking the kth learning task as an example, and updating the parameters as follows:
in formula (II), theta'kFor the updated weight coefficient vector, theta is the initial weight coefficient vector, alpha is the learning rate, which can be given artificially,
representing the gradient of the objective function.
9. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 8, wherein the seventh step is specifically as follows:
in order to obtain a generalization model adapting to water absorption profile prediction, an integrated multi-task objective function is established on the basis of a neural network model after initial learning, and the form of the integrated multi-task objective function is as follows:
and (3) carrying out optimization solution on the objective function of the formula (13) by using a gradient descent algorithm to obtain the weight of the generalized model, wherein the parameter updating process comprises the following steps:
wherein θ is a vector of the weight coefficients of the generalized model,
gradient representing the objective function, NlayerRepresents the number of small layers, and β is the learning rate.
10. The method for predicting the water absorption profile based on the small sample condition as claimed in claim 9, wherein the ninth step is specifically as follows:
(1) generalized model-based objective function establishment
The objective function is similar to the objective function of a single learning task established in the step five, but the difference is that the predicted value in the objective function is the generalized model obtained in the step seven, and the specific equation form is as follows:
wherein m represents the number of samples of the target small layer, hθ(xi) Representing the predicted value of the generalized neural network model, and theta represents the weight coefficient of the generalized neural network model;
(2) personalized learning based on small sample data
Based on the limited water absorption profile data of the small layer, the parameters of the neural network model are quickly adjusted, and the parameter updating process is as follows:
in the formula, thetai+1,θiRespectively representing model parameters in the i +1 th and i th iteration steps,
expressing the gradient of the objective function, and gamma is the learning rate;
(3) calculation of water absorption profile of water injection well
Replacing the target small layer, repeating the fine adjustment of the parameters to obtain an individual water absorption prediction model suitable for each small layer of the water injection well, and calculating the percentage d of the water absorption of the small layer to the injection amount of the water injection well according to a formula (17)kThe relative water absorption is obtained, and a water absorption profile of the water injection well is drawn according to the relative water absorption;
in the formula (d)kIs the relative water absorption of each k th small layer of the water injection well, qkThe water absorption amount of the kth small layer is shown, and K is the number of perforation layers of the water injection well.
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