CN110941890B - Offshore oil reservoir dynamic real-time production optimization method based on optimal control theory - Google Patents
Offshore oil reservoir dynamic real-time production optimization method based on optimal control theory Download PDFInfo
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Abstract
The invention discloses an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory, which comprises the following steps: establishing an oil reservoir digital-analog model by using Eclipse software; establishing an oil reservoir dynamic real-time optimization mathematical model; establishing constraint conditions of a mathematical model, including the limitation of the integral planning of an oil field, the limitation of the integral injection and production capacity of an oil reservoir and the limitation of the injection and production capacity of a single well; selecting an optimization algorithm for solving the model, wherein the optimization algorithm comprises an SPSA gradient algorithm and a projection gradient method; and calling an oil reservoir digital-analog model for iterative computation. The problems of complex oil-water distribution, high potential difficulty of residual oil, difficult production adjustment in the middle and later development stages and the like are faced in the high water-cut period of the offshore oil field, the stable yield of the offshore oil field can be maintained, and the development cost can be reduced.
Description
Technical Field
The invention relates to a method, in particular to an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory.
Background
At present, how to further deeply research, optimize a production development scheme and improve injection-production contradiction for an offshore river facies reservoir stratum in a high water cut period based on the existing conditions is the key for realizing oil and water stabilization and improving development benefits.
In the prior art, an oil reservoir engineering method is utilized, and an oil reservoir numerical simulation technology is combined to research oil reservoir pressure change, water injection effectiveness and well pattern adaptability; carrying out oil extraction system research from the lowest reasonable flowing pressure, the reasonable production pressure difference and the reasonable liquid production strength of the production well; and (4) carrying out research on a water injection system, and demonstrating the fracture pressure of an oil layer, the injection pressure, the injection quantity and the reasonable water injection strength of the water injection well. And comprehensively comparing and analyzing the simulation result through repeated fitting and prediction, and finally, preferably selecting an optimal development scheme. However, a large amount of static and dynamic data needs to be collected and processed in the process, and the research result is not accurate due to the imperfection of the data and the limitation of some empirical algorithms; when the optimal scheme is optimized by using the oil reservoir numerical simulation technology, the fitting time is long, the requirement on a computer is high, the whole block or the whole mining unit is often optimized integrally, and the selected development control parameters are not necessarily the most suitable for a single well; the control parameters of each well are modified manually to optimize the parameters of a single well, the workload is increased exponentially, the problems of non-convergence of an algorithm and the like occur, and time and labor are wasted.
In summary, the prior art is characterized in that the optimization design of the manual water injection and oil extraction scheme is carried out by means of an oil reservoir engineering method or a numerical simulation technology, the randomness of the method is strong, the scheme of the manual design of limited combination is often not optimal, the numerical simulation model is complex to establish, the manual history fitting process consumes time and labor, the optimization design workload is large, a large amount of manpower and material resources are consumed, and the ideal effect cannot be obtained. The optimal value can only be found in the limited combination of the design, but not the real optimal value, which has certain limitation, and the workload is large, so that the time and the labor are wasted.
Disclosure of Invention
The invention aims to solve the problems of complex oil-water distribution, high residual oil potential difficulty, difficult production adjustment in the middle and later periods of development and the like in a high water-cut period of an offshore oil field, and provides an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory by utilizing the existing data mining machine learning algorithm in order to keep stable yield of the oil field and reduce development cost.
The purpose of the invention is realized by the following technical scheme.
The invention relates to an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory, which comprises the following steps of:
the first step is as follows: establishing an oil reservoir digital-analog model
An oil reservoir digital-analog model is established by Eclipse software, and a model file comprises the following contents:
1) Data, base: the main file of the digital-analog model is used for digitizing the oil reservoir, simulating the oil-water flow relationship of the oil reservoir and predicting the production dynamics of the oil reservoir;
2) init. Inc file: the field files of the digital-analog model comprise SGAS, PRES, SWAT and RS model field files;
3) sch.inc document: the dynamic file of the oil-water well production of the digital-analog model comprises the working system, the prediction time and the step length of the oil-water well;
4) ZSQ _ GIRD file: grid data of the digital-analog model after history fitting;
5) Restarting the file: exporting and sorting the model data body to be restarted again, independently making the model data body into a data body, and directly starting to operate from the first year of optimization, avoiding the continuous calling of the restart file and saving time;
the second step is that: establishing oil reservoir dynamic real-time optimization mathematical model
Objective function (NPV) = oil price x cumulative oil production-cost of water injection and production-other costs
Wherein J is net present value, ten thousand yuan; u is a control variable vector; y is a reservoir geological static parameter; m is an oil reservoir production dynamic parameter; l is the control step number in the oil reservoir production time; n is a radical ofPThe number of production wells; n is a radical of hydrogenIThe number of water injection wells; r isoThe unit price of crude oil is ten thousand yuan/ton; r iswTen thousand yuan/ton for the treatment cost of the produced water; r iswiCost of water injection, ten thousand yuan/ton; q. q.soFor the accumulated oil production, ton; q. q.swTon of water is produced; q. q.swiAccumulating water and feeding in tons; t is the self-defined time; Δ t is a time period; b is annual rate,%;
the third step: constraint condition for establishing mathematical model
1) Limitation of oil field overall planning: e.g. of the typei(u,y,m)＝0；
2) And (3) limiting the integral injection and production amount of the oil reservoir: c. Cj(u,y,m)≤0；
3) Limitation of single well injection and production capacity:
in the formula (I), the compound is shown in the specification,
and
respectively represent the k-th control variable ukThe upper and lower boundaries of (c); e.g. of the typei(u, y, m) =0 and cjThe (u, y, m) is less than or equal to 0 and is respectively an equality constraint condition and an inequality constraint condition;
the fourth step: selecting an optimization algorithm for solving a model
The constraint conditions of the oil reservoir dynamic real-time optimization mathematical model in the second step and the constraint conditions of the mathematical model in the third step jointly form an oil reservoir dynamic real-time optimization mathematical model considering the actual limit conditions of oil reservoir development; selecting the following two optimization algorithms, respectively determining the searching direction and the size of the control variable, and further solving a mathematical model;
1) SPSA gradient algorithm: the search direction is the direction of ascent and the expected value is the true gradient
The actual injection-production parameters often have certain correlation in time, and Bernoulli distribution vectors are completely independent of each other, so that the obtained scheme has strong volatility; for this purpose, a control variable covariance matrix C is introducedUGenerating a new disturbance vector and carrying out continuous processing;
smoothing the control variable;
gaussian model:
in the formula, gl(ul) Is an objective function in ulA gradient function of (a); u. oflThe optimal control variable of the first iteration step; l is an iteration step; j (u)l) Is ulAn objective function of (d); epsilonlIs the disturbance step length; deltalIs a disturbance vector, is a +/-1 Bernoulli distribution; cUAn N-dimensional control variable covariance matrix; zlDisturbance vectors which are subject to standard normal distribution; cU 1/2Is an N-dimensional lower triangular square matrix; ci,jThe correlation value when the time step is i, j; σ is the standard deviation; a is a time correlation length;
2) Projection gradient method: when the iteration point is positioned on the boundary of the feasible region and the gradient direction of the iteration point points to the outside of the feasible region, taking the projection of the iteration point on the boundary as a search direction;
in the formula, slGenerating unknown gradients J for random perturbationsM(sl) When the gradient is approached, a new estimation value is obtained; alpha is the calculation step length;
the difference between the objective function and the calculated value; p is the direction of the structural negative gradient; i is an identity matrix;
a matrix formed by the total water injection amount and the total liquid production amount of the oil reservoir at the n moments; t is matrix transposition; nu denotes a number, e.g. uNuRepresents the Nu variable;
the fifth step: invoking an oil reservoir digital-analog model for iterative computation
The optimization algorithm of the fourth step can continuously adjust the working system of the oil-water well (namely the injection quantity of the water injection well and the liquid yield of the oil production well) under the constraint condition of the third step, so that the working system of each development well can be changed in real time at each time step; then the optimization algorithm calls Eclipse software to calculate the final oil accumulation amount, water accumulation amount and water accumulation amount results of the oil deposit digital-analog model established in the first step, and returns the calculation results to the oil deposit dynamic real-time optimization mathematical model established in the second step to calculate economic benefits (net present value NPV); and finally, according to whether the calculated economic benefit result is optimal or not, providing a new oil-water well working system, carrying out iterative optimization, and continuously carrying out cyclic operation until the oil-water well optimal working system capable of realizing the maximum economic benefit is obtained.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
the invention relates to an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory, which is used for designing an injection-production adjustment scheme by applying a new oil reservoir development dynamic real-time optimization method.
Compared with the conventional numerical simulation method, the method can quickly, accurately and efficiently optimize the working system of the oil well and the water well, and can optimize and adjust in real time. The method is applied and verified in a certain block in south China sea, and a good effect is achieved.
Drawings
FIG. 1 is a computational flow diagram of the present invention.
FIG. 2 is a graph showing a comparison of the residual oil distribution before and after prediction for each small layer.
FIG. 3 is a comparison of the abundance distribution of reserves before and after prediction for each small layer.
Detailed Description
The invention will be further illustrated by the following non-limiting examples, without thereby restricting the invention to the scope of the examples described. The invention is further described below with reference to the accompanying drawings.
The invention is based on the optimal control theory and the oil reservoir numerical simulation technology, combines the geological oil reservoir characteristics of the offshore oil field, applies a new oil reservoir development dynamic real-time optimization method to carry out injection-production adjustment scheme design, has the greatest advantages that a complex oil reservoir development system can be described as an optimal control problem from the long-term oil reservoir development benefit, production regulation parameters of each stage of an oil-water well can be automatically calculated through an optimal control algorithm, the optimal regulation scheme is rapidly provided for oil field development and production, the oil reservoir development condition is efficiently managed and improved, the problems of complex oil-water distribution, high residual oil potential difficulty, difficult production adjustment in the middle and later development stages and the like in the high water cut stage of the offshore oil field can be particularly solved, the stable production of the offshore oil field can be maintained, and the development cost can be reduced. Compared with the conventional numerical simulation method, the novel method can quickly, accurately and efficiently optimize the working system of the oil well and the water well and can optimize and adjust in real time. The method is applied and verified in a certain block in south China sea, and a good effect is achieved.
The invention relates to an offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory, wherein a calculation flow chart is shown in figure 1, and the method specifically comprises the following steps:
the first step is as follows: establishing an oil reservoir digital-analog model
An oil reservoir digital-analog model is established by Eclipse software, and a model file comprises the following contents:
1) Data, base: and the main file of the digital-analog model is used for digitizing the oil reservoir, simulating the oil-water flow relationship of the oil reservoir and predicting the production dynamics of the oil reservoir.
2) init. Inc file: the field files of the digital-analog model comprise model field files such as SGAS, PRES, SWAT and RS.
3) Inc document: the dynamic file of oil-water well production of the digital-analog model mainly comprises the working system, the predicted time, the step length and the like of the oil-water well.
4) ZSQ _ GIRD file: and (5) grid data of the digital-analog model after history fitting.
5) And (4) restarting the file: exporting and sorting the model data body to be restarted again, independently making the model data body into a data body, and directly starting to operate from the first year of optimization, avoiding the continuous calling of the restart file and saving time;
the second step is that: establishing oil reservoir dynamic real-time optimization mathematical model
The model establishment mechanism is as follows: the method aims at realizing maximization of economic benefits (namely net present value NPV) of the oil reservoir, describes control over an oil reservoir production system into an optimization problem, solves the problem by optimizing injection and production parameters of an oil-water well, obtains an optimal control scheme, regulates and controls injection and production amount of the oil-water well, and realizes optimization of oil reservoir development.
Objective function (NPV) = oil price x cumulative oil production-cost of water injection and production-other costs
Wherein J is net present value, ten thousand yuan; u is a control variable vector; y is a reservoir geological static parameter; m is an oil reservoir production dynamic parameter; l is the control step number in the oil reservoir production time; n is a radical of hydrogenPThe number of production wells; n is a radical ofIThe number of water injection wells; r isoThe unit price of crude oil is ten thousand yuan/ton; r iswTen thousand yuan/ton for the treatment cost of the produced water; r iswiCost of water injection, ten thousand yuan/ton; q. q.soOil production is accumulated, and ton is realized; q. q.swTon of water is produced; q. q.swiTon of accumulated water is injected; t is the self-defined time; Δ t is a time period; b is annual percentage rate,%.
The third step: establishing constraint conditions of mathematical model
Aiming at the oil reservoir dynamic real-time optimization mathematical model in the second step, the oil reservoir dynamic real-time optimization mathematical model is combined with the actual limiting conditions in the oil reservoir development process by establishing the constraint conditions, namely, the objective function J is maximized by optimizing the control variable u under the condition of meeting the constraint conditions. The constraint conditions mainly comprise the limitation of the whole oil field planning (such as annual oil field planning oil production, planning water injection and the like), the limitation of the whole oil reservoir injection and production (the injection quantity and the liquid production are limited due to the limited processing capacity of an offshore platform) and the limitation of the single-well injection and production capacity (the single-well injection and production capacity is limited due to the influence of reservoir conditions).
1) And (3) constraint of an equation: limits on the overall planning of an oil field ej(u,y,m)＝0
2) The inequality constrains: limitation of the overall injection and production of an oil reservoir cj(u,y,m)≤0
3) And (3) boundary constraint: limitation of single well injection and production capacity
In the formula (I), the compound is shown in the specification,
and
respectively represent the kth control variable ukThe upper and lower boundaries of (c); e.g. of the typei(u, y, m) =0 and cjAnd (u, y, m) is less than or equal to 0 and is respectively an equality constraint condition and an inequality constraint condition.
The fourth step: selecting an optimization algorithm for solving a model
And the oil reservoir dynamic real-time optimization mathematical model in the second step and the constraint conditions of the mathematical model in the third step form the oil reservoir dynamic real-time optimization mathematical model considering the actual limit conditions of oil reservoir development. And then, comparing a plurality of algorithms, selecting the following two optimization algorithms, respectively determining the searching direction and size of the control variable, and further solving the mathematical model.
1) SPSA gradient algorithm: the search direction is the direction of ascent and the expected value is the true gradient
The actual injection-production parameters often have certain correlation in time, and Bernoulli distribution vectors are completely independent of each other, so that the obtained scheme has strong volatility; for this purpose, a control variable covariance matrix C is introducedUGenerating a new disturbance vector and carrying out continuous processing;
and smoothing the control variable.
Gaussian model:
in the formula, gl(ul) Is an objective function in ulA gradient function of (a); u. oflThe optimal control variable of the first iteration step; l is an iteration step; j (u)l) Is ulAn objective function of (d); epsilonlIs the disturbance step length; deltalIs a disturbance vector, is a +/-1 Bernoulli distribution;CUan N-dimensional control variable covariance matrix; zlDisturbance vectors which are subject to standard normal distribution; cU 1/2Is an N-dimensional lower triangular square matrix; ci,jThe correlation value when the time step is i, j; σ is the standard deviation; a is the time correlation length.
2) Projection gradient method: when the iteration point is located on the boundary of the feasible region and the gradient direction of the iteration point points to the outside of the feasible region, the projection of the iteration point on the boundary is taken as the search direction.
In the formula, slGenerating unknown gradients J for random perturbationsM(sl) When the gradient is approached, a new estimation value is obtained; alpha is the calculation step length;
is the difference between the target function and the calculated value; p is the direction of the structural negative gradient; i is an identity matrix;
a matrix formed by the total water injection quantity and the total liquid production quantity of the oil reservoir at the moment n; t is matrix transposition; nu denotes a number, e.g. uNuRepresents the Nu number of variables.
The fifth step: invoking an oil reservoir digital-analog model for iterative computation
The optimization algorithm of the fourth step can continuously adjust the working system of the oil-water well (namely the injection quantity of the water injection well and the liquid yield of the oil production well) under the constraint condition of the third step, so that the working system of each development well can be changed in real time at each time step; then the optimization algorithm calls Eclipse software to calculate the final oil accumulation amount, water accumulation amount and water accumulation amount results of the oil deposit digital-analog model established in the first step, and returns the calculation results to the oil deposit dynamic real-time optimization mathematical model established in the second step to calculate economic benefits (net present value NPV); and finally, according to whether the calculated economic benefit result is optimal or not, providing a new oil-water well working system, carrying out iterative optimization, and continuously carrying out cyclic operation until the oil-water well optimal working system capable of realizing the maximum economic benefit is obtained.
Example 1:
the dynamic real-time production optimization technology of offshore oil reservoirs in south China sea A oil fields based on an optimal control theory.
The A oil field structure is a low-amplitude anticline structure, the east is high, the west is low, two broken layer groups running in parallel are arranged at the north, and edge water is supplied between the broken layers. In the range of oil-containing area, the north side is fault and oil-water interface control boundary, the west side is oil-water interface, the east side is work area boundary, and the south side is lithologic boundary. Normal warm-pressing system, side water reservoir; the average porosity is 18 percent, and the permeability is 400-800mD.
The oil field is put into development in 2014 in 10 months, and up to the present, 15 production wells are put into production, and the daily oil production is 2900m3D, 15% of comprehensive water content and 195m of average daily oil production of single well3D, cumulative oil 117X 104m3. The water in the A oil field comes from the north and the west, the energy of the water body is weak, the pressure supply required by the integral development of the oil reservoir is difficult to effectively provide, the pressure of the oil well is reduced quickly, and the energy is supplemented by water injection. And injecting water into the area of the reverse nine-point injection and production well network, injecting 4 wells in the initial stage, injecting 15 wells in the 4-point injection stage, and enabling the injection and production well ratio to be 1:3.
The optimized production data comprises oil yield, water yield, crude oil price, water injection cost and water well injection amount of the oil well, so that better economic benefit can be obtained. Well track, completion horizon, measure horizon and measure content of each well. The optimization start time was 2015 for 8 months, and 5-year production measures were expected to be optimized.
In the fine geologic modeling phase of the reservoir, although much work has been done, there may be a large discrepancy between the dynamic data generated by the simulation and the actual dynamics due to inaccuracies and uncertainties in certain parameters (e.g., permeability of the reservoir). Therefore, optimization needs to be based on a history-fitted model, combine with the definition of an objective function, and utilize an optimization algorithm to change input variables such as water injection amount, production amount, and the like, so as to obtain a relatively optimal optimization result within a relatively limited optimization time.
Based on the continuous change of the production dynamics of the oil reservoir, the actual oil reservoir is optimized in sections at different time periods, and the optimization result is observed. From the comparison graphs (such as fig. 2 and fig. 3) of the residual oil and the reserve abundance distribution before and after prediction of each small layer, it can be seen that the recovery ratio of the residual oil is greatly improved and the effect is obvious when a model after 5 years is predicted compared with the original unpredicted calculation result.
The research results guide the dynamic real-time production optimization of the offshore oil deposit of the oil field A based on the optimal control theory, good effects are obtained, the problem is solved by optimizing the injection and production parameters of the oil-water well, an optimal control scheme is obtained, and the effects of oil stabilization and water control are obvious.
Although the present invention has been described with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, and those skilled in the art can make various modifications without departing from the spirit and scope of the present invention as defined in the appended claims.
Claims (1)
1. An offshore oil reservoir dynamic real-time production optimization method based on an optimal control theory is characterized by comprising the following steps:
the first step is as follows: establishing an oil reservoir digital-analog model
An oil reservoir digital-analog model is established by Eclipse software, and a model file comprises the following contents:
1) Data, base: the main file of the digital-analog model is used for digitizing the oil reservoir, simulating the oil-water flow relationship of the oil reservoir and predicting the production dynamics of the oil reservoir;
2) init. Inc file: the field files of the digital-analog model comprise SGAS, PRES, SWAT and RS model field files;
3) Inc document: the dynamic file of the oil-water well production of the digital-analog model comprises the working system, the prediction time and the step length of the oil-water well;
4) ZSQ _ GIRD file: grid data of the digital-analog model after history fitting;
5) Restarting the file: exporting and sorting the model data body to be restarted again, independently making the model data body into a data body, and directly starting to operate from the first year of optimization, avoiding the continuous calling of the restart file and saving time;
the second step is that: establishing oil reservoir dynamic real-time optimization mathematical model
Objective function (NPV) = oil price x accumulated oil production-cost of water injection and production-other costs
Wherein J is net present value, ten thousand yuan; u is a control variable vector; y is a reservoir geological static parameter; m is an oil reservoir production dynamic parameter; l is the control step number in the oil reservoir production time; n is a radical ofPThe number of production wells; n is a radical ofIThe number of water injection wells; r isoThe unit price of crude oil is ten thousand yuan/ton; r is a radical of hydrogenwTen thousand yuan/ton for the treatment cost of the produced water; r iswiCost of water injection, ten thousand yuan/ton; q. q.soOil production is accumulated, and ton is realized; q. q.swTon of water is produced; q. q.swiTon of accumulated water is injected; t is the self-defined time; Δ t is a time period; b is annual rate,%;
the third step: establishing constraint conditions of mathematical model
1) Limitation of oil field overall planning: e.g. of the typei(u,y,m)＝0；
2) And (3) limiting the integral injection and production amount of the oil reservoir: c. Cj(u,y,m)≤0；
3) Limitation of single well injection and production capacity:
in the formula (I), the compound is shown in the specification,
and
respectively represent the k-th control variable ukThe upper and lower boundaries of (c); e.g. of the typei(u, y, m) =0 and cjThe (u, y, m) is less than or equal to 0 and is respectively an equality constraint condition and an inequality constraint condition;
the fourth step: selecting an optimization algorithm for solving a model
The oil reservoir dynamic real-time optimization mathematical model in the second step and the constraint conditions of the mathematical model in the third step form an oil reservoir dynamic real-time optimization mathematical model considering the actual limit conditions of oil reservoir development; selecting the following two optimization algorithms, respectively determining the search direction and the size of a control variable, and further solving a mathematical model;
1) SPSA gradient algorithm: the search direction is the direction of ascent and the expected value is the true gradient
The actual injection-production parameters often have certain correlation in time, and Bernoulli distribution vectors are completely independent of each other, so that the obtained scheme has strong volatility; for this purpose, a control variable covariance matrix C is introducedUGenerating a new disturbance vector and carrying out continuous processing;
smoothing the control variable;
gaussian model:
in the formula, gl(ul) Is an objective function in ulA gradient function of (a); u. oflThe optimal control variable for the first iteration step; l is an iteration step; j (u)l) Is ulAn objective function of (d); epsilonlIs the disturbance step length; deltalIs a disturbance vector, is a +/-1 Bernoulli distribution; cUAn N-dimensional control variable covariance matrix; zlDisturbance vectors which are subject to standard normal distribution; cU 1/2Is an N-dimensional lower triangular square matrix; ci,jThe correlation value when the time step is i, j; σ is the standard deviation; a is the time-dependent length;
2) Projection gradient method: when the iteration point is positioned on the boundary of the feasible region and the gradient direction of the iteration point points to the outside of the feasible region, taking the projection of the iteration point on the boundary as a search direction;
in the formula, slGenerating unknown gradients J for random perturbationsM(sl) When the gradient is approached, a new estimation value is obtained; alpha is the calculation step length;
the difference between the objective function and the calculated value; p is the direction of the structural negative gradient; i is an identity matrix;
a matrix formed by the total water injection amount and the total liquid production amount of the oil reservoir at the n moments; t is matrix transposition; nu denotes a number, e.g. uNuRepresents the Nu variable;
the fifth step: invoking an oil reservoir digital-analog model for iterative computation
The optimization algorithm of the fourth step can continuously adjust the working system of the oil-water well (namely the injection quantity of the water injection well and the liquid yield of the oil production well) under the constraint condition of the third step, so that the working system of each development well can be changed in real time at each time step; then the optimization algorithm calls Eclipse software to calculate the final oil accumulation amount, water accumulation amount and water accumulation amount results of the oil deposit digital-analog model established in the first step, and returns the calculation results to the oil deposit dynamic real-time optimization mathematical model established in the second step to calculate economic benefits (net present value NPV); and finally, according to whether the calculated economic benefit result is optimal or not, providing a new oil-water well working system, carrying out iterative optimization, and continuously carrying out cyclic operation until the oil-water well optimal working system capable of realizing the maximum economic benefit is obtained.
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