A method for balanced regulation and control of water invasion flow field in three-layer horizontal wells in a strongly heterogeneous low-permeability tight sandstone gas reservoir

Abstract

The present invention relates to a method for balanced regulation and control of the water invasion flow field of a three-layer horizontal well in a strongly heterogeneous low-permeability tight sandstone gas reservoir, including respectively simulating the water invasion processes of the low-permeability layer, the medium-permeability layer, and the high-permeability layer through a streamline numerical simulation method of a modified Pollock streamline tracing algorithm that couples gas compressibility, and obtaining the water invasion parameters of each layer; respectively calculating the comprehensive water invasion evaluation indexes of each layer according to the water invasion parameters of each layer; respectively determining the risk levels of each layer according to the comprehensive water invasion evaluation indexes of each layer; constructing a mathematical model for regulating and controlling the multi-layer and multi-well water invasion flow field; and using an adaptive covariance matrix evolution algorithm to iteratively optimize and minimize the standard deviation of the water invasion front advance speed of each layer in the mathematical model for regulating and controlling the multi-layer and multi-well water invasion flow field, and obtaining the production of each layer. The present invention realizes the transparent monitoring and intelligent regulation and control of the water invasion flow field, greatly reduces the influence of water invasion on the gas well productivity, extends the water-free gas production period of the gas reservoir, and at the same time improves the overall recovery rate, and has good popularization and application value.

Description

Technical Field

[0001] The invention relates to a balanced control method for water intrusion field in three-layer horizontal wells of a highly heterogeneous low-permeability dense sandstone gas reservoir, and belongs to the field of oil and gas field development. Background Art

[0002] In recent years, as the difficulty of developing conventional oil and gas resources increases, low-permeability tight sandstone gas reservoirs have gradually become an important area for increasing natural gas production. However, such gas reservoirs generally have the characteristics of strong reservoir heterogeneity, developed natural fractures, and active edge and bottom water. Water invasion is very likely to occur during the development process, resulting in a rapid decline in gas well production capacity and a significant reduction in gas reservoir recovery. With the maturity of horizontal well technology, the multi-layer horizontal well development model has become an important means to improve the degree of reservoir utilization and optimize the development effect of gas reservoirs. However, in water-invaded sandstone gas reservoirs, the flow field distribution of multi-layer horizontal wells is affected by reservoir physical property differences, water invasion direction, and wellbore pressure drop. It is easy to have severe water invasion in local layers and uneven contribution of production layers, which in turn aggravates the production attenuation of gas wells. Therefore, how to realize intelligent regulation of multi-layer horizontal wells under the background of water invasion, balance flow field distribution, and improve development efficiency has become an important research topic in the current development of oil and gas fields.

[0003] At present, conventional streamline simulation methods do not take into account the changes in gas high-pressure physical properties, resulting in large errors in the prediction of the water invasion front. Traditional horizontal well flow field control methods mainly rely on surface throttling, downhole stratified production and mechanical flow limiting devices. These methods often have limitations such as delayed response, insufficient control accuracy, and difficulty in real-time adaptation to dynamic changes in gas reservoirs. Traditional optimization methods are difficult to deal with high-dimensional nonlinear constraint problems in multi-layer and multi-well systems, are prone to falling into local optimality, and take a long time to calculate, and cannot support real-time decision-making on site. Therefore, there is an urgent need for an intelligent flow field control method that can combine real-time production data, gas reservoir dynamic evolution laws and artificial intelligence optimization algorithms to achieve precise control of multi-layer horizontal wells, optimize flow field distribution, delay water invasion breakthroughs, and improve the ultimate recovery rate. Summary of the invention

[0004] The purpose of the present invention is to address the problems existing in the prior art and to provide a method for balanced regulation of water invasion flow field in three-layer horizontal wells in highly heterogeneous, low-permeability, and dense sandstone gas reservoirs. The method realizes transparent monitoring and intelligent regulation of the water invasion flow field, greatly reduces the impact of water invasion on the production capacity of gas wells, extends the water-free gas production period of the gas reservoir, and at the same time improves the overall recovery rate, which has good promotion and application value.

[0005] The technical solution provided by the present invention to solve the above technical problems is: a method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability dense sandstone gas reservoirs, comprising the following steps:

[0006] Step S10: Use the streamline numerical simulation method of the modified Pollock streamline tracing algorithm that couples gas compressibility to simulate the water invasion processes of the low-permeability layer, medium-permeability layer, and high-permeability layer respectively, and obtain the water invasion parameters of each layer;

[0007] Step S20: Calculate the comprehensive water invasion evaluation indexes of the wells where each layer is located respectively according to the water invasion parameters of each layer;

[0008] Step S30: Determine the risk levels of the wells where each layer is located respectively according to the comprehensive water invasion evaluation indexes of the wells where each layer is located;

[0009] Step S40: Construct a mathematical model for multi-layer and multi-well water invasion flow field regulation;

[0010] Step S50: Use the adaptive covariance matrix evolution algorithm in the mathematical model for multi-layer and multi-well water invasion flow field regulation to iteratively optimize and minimize the standard deviation of the water invasion front advance velocity of each layer, and obtain the production of each layer.

[0011] A further technical solution is that the seepage differential equation of the modified Pollock streamline tracing algorithm that couples gas compressibility in the step S10 is:

[0012]

[0013] In the formula: is the formation permeability; is the natural gas viscosity; is the pressure; is the porosity; t is the time; Z is the absolute pressure of the gas.

[0014] A further technical solution is that the comprehensive water invasion evaluation indexes include the water invasion volume coefficient, the water invasion front advance velocity, and the water invasion streamline density index.

[0015] A further technical solution is that the calculation formula of the water invasion volume coefficient is:

[0016]

[0017] In the formula: is the water invasion volume coefficient; is the water invasion amount; is the time; is the pressure drop;

[0018] The calculation formula of the water invasion front advance velocity is:

[0019]

[0020] In the formula: is the water invasion front advance velocity; is the advancing distance of the water invasion front within the time;

[0021] The calculation formula of the water invasion streamline density index is as follows:

[0022]

[0023] In the formula: is the water invasion streamline density index; is the number of water invasion streamlines in this layer; is the total number of streamlines.

[0024] A further technical solution is that in step S30, the water invasion comprehensive evaluation index of each well where each layer is located is calculated respectively R , and the risk level of each layer is judged according to the water invasion comprehensive evaluation index R of each well where each layer is located; among them, the water invasion risks of each well where each layer is located are divided into three levels, R If the value is in the top 30% quantile of all horizons, it is identified as a high risk; R If the value is between 30% - 70% of all horizons, it is identified as a medium risk; R If the value is in the bottom 30% quantile of all horizons, it is identified as a low risk.

[0025] A further technical solution is that the calculation formula of the water invasion comprehensive evaluation index R is as follows:

[0026]

[0027] In the formula: R is the water invasion comprehensive evaluation index; is the water invasion volume coefficient; is the advancing speed of the water invasion front; is the water invasion streamline density index.

[0028] A further technical solution is that in the multi-layer and multi-well water invasion flow field regulation mathematical model, the core objective function is to minimize the standard deviation of the advancing speed of the water invasion front of each layer, the production of each layer is used as the optimization variable, and the risk level of each layer is used as the constraint condition.

[0029] A further technical solution is that the formula for minimizing the standard deviation of the advancing speed of the water invasion front of each layer is:

[0030]

[0031] In the formula: N is the number of reservoirs; is the standard deviation of the advancing speed of the water invasion front; is the kAdvancing velocity of the water invasion front of the layer; It is the arithmetic mean of the advancing velocities of the water invasion fronts of all layers.

[0032] A further technical solution is that the constraint conditions in the mathematical model for regulating the multi-layer and multi-well water invasion flow field are as follows:

[0033] When the risk level is low risk, the constraint condition is to increase production in the next time step;

[0034] When the risk level is medium risk, the constraint condition is to impose additional constraints;

[0035] When the risk level is high risk, the constraint condition is to reduce production in the next time step.

[0036] Beneficial effects of the present invention: Aiming at problems such as severe water invasion, strong reservoir heterogeneity, and uneven production of multiple layers, the present invention constructs a full-process technical system including compressibility-coupled streamline simulation, intelligent optimization algorithm, and automated production regulation. Through the streamline numerical simulation technology coupling gas compressibility, accurate prediction of the water invasion front is achieved; based on multi-dimensional water invasion evaluation indexes, the dynamic differences of water invasion in each layer are quantitatively characterized; combined with the improved intelligent optimization algorithm, a differential production regulation scheme is formed.

[0037] The application results show that this method effectively balances the water invasion displacement process of the multi-layer gas reservoir, significantly inhibits the local water channeling phenomenon, improves the reserve utilization degree of the low-permeability layer, and provides reliable technical support for the long-term stable production and efficient development of the gas reservoir. Description of the Drawings

[0038] Figure 1 It is the flow chart of the method for balancing and regulating the water invasion flow field of three horizontal wells in a strongly heterogeneous low-permeability tight sandstone gas reservoir of the present invention;

[0039] Figure 2 It is the reservoir permeability distribution and well location distribution diagram in a specific embodiment of the present invention;

[0040] Figure 3 It is the water invasion streamline simulation result diagram in a specific embodiment of the present invention;

[0041] Figure 4 It is the water invasion front distribution diagram before flow field regulation in a specific embodiment of the present invention;

[0042] Figure 5 It is the flow chart of the adaptive covariance matrix evolution algorithm of the present invention;

[0043] Figure 6 It is the water invasion front distribution diagram after flow field regulation in a specific embodiment of the present invention. Detailed Embodiments

[0044] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] As Figure 1 shown, a method for balanced regulation of water invasion flow field of three-layer horizontal wells in a strongly heterogeneous low-permeability tight sandstone gas reservoir provided by the present invention includes the following steps:

[0046] Step S10: Respectively simulate the water invasion processes of the low-permeability layer, the medium-permeability layer, and the high-permeability layer by a streamline numerical simulation method of a modified Pollock streamline tracing algorithm that couples gas compressibility, and obtain the water invasion parameters of each layer;

[0047] The commonly used Pollock algorithm in streamline simulation is mainly based on the assumption of fluid incompressibility. However, gas has obvious compressibility, which is manifested in that the volume and density of gas are significantly affected by factors such as pressure and temperature. The state equation of an ideal gas can be expressed by Boyle-Gay-Lussac's law:

[0048] (1)

[0049] In the formula: is the absolute pressure of the gas; is the gas constant; is the thermodynamic temperature.

[0050] An ideal gas is an idealized model that ignores the intermolecular forces. There will be a certain deviation in the compressibility of an actual gas, and its state equation is:

[0051] (2)

[0052] In the formula: is the absolute pressure of the gas.

[0053] The gas motion equation can be divided into linear seepage and non-linear seepage. For linear seepage, its flow law can be expressed by the generalized Darcy's law:

[0054] (3)

[0055] In three-dimensional space, the three components of the seepage velocity are respectively expressed as:

[0056] (4)

[0057] (5)

[0058] (6)

[0059] In the formula: is the seepage velocity; is the formation permeability; is the natural gas viscosity; is the pressure; is the gas density; is the acceleration of gravity; and and are the spatial coordinate directions.

[0060] When the seepage velocity of the gas increases to a certain extent, the influence of turbulence and inertia is significantly enhanced, and the seepage no longer satisfies Darcy's law. The relationship between the non-linear seepage pressure gradient and the seepage velocity is:

[0061] (7)

[0062] In the formula: is the pore structure characteristic parameter affecting turbulence and inertial resistance.

[0063] The continuity equation of gas seepage can be expressed as:

[0064] (8)

[0065] In the formula: is the porosity; is the time.

[0066] In summary, the seepage differential equation of real gas can be expressed as:

[0067] (9)

[0068] The modified Pollock streamline tracking algorithm considering gas compressibility proposed by the present invention can more accurately simulate the gas-water two-phase flow characteristics in high-pressure gas reservoirs by dynamically coupling the absolute pressure of the gas, providing a reliable basis for subsequent intelligent regulation.

[0069] Taking the three-layer sandstone water-invaded gas reservoir mechanism model as shown in Figure 2 as an example, streamline numerical simulation is carried out. The streamline distribution results are as shown in Figure 3 Before flow field regulation, the water invasion front distribution is as shown in Figure 4 ;

[0070] Step S20: Calculate the water invasion comprehensive evaluation index of each well in each layer according to the water invasion parameters of each layer;

[0071] The water invasion comprehensive evaluation index includes the water invasion volume coefficient, the water invasion front advance velocity, and the water invasion streamline density index.

[0072] The water influx volume coefficient is defined as the water influx volume generated per unit pressure drop per unit time, representing the water influx intensity and the affected range:

[0073] (10)

[0074] In the formula: is the water influx volume coefficient; is the water influx amount; is the time; is the pressure drop.

[0075] The advancing speed of the water influx front is defined as the advancing distance of the water influx front towards the gas well per unit time, representing the dynamic speed of water influx:

[0076] (11)

[0077] In the formula: is the advancing speed of the water influx front; is the advancing distance of the water influx front at time.

[0078] The water influx streamline density index is defined as the ratio of the number of water influx streamlines to the total number of streamlines per unit area, representing the distribution of preferential water influx channels:

[0079] (12)

[0080] In the formula: is the water influx streamline density index; is the number of water influx streamlines in this layer; is the total number of streamlines.

[0081] The water influx volume coefficient, the advancing speed of the water influx front, and the water influx streamline density index are respectively normalized, and the comprehensive water influx evaluation indexes of each layer are shown in Table 1.

[0082] Table 1 Normalized results of comprehensive water influx evaluation indexes of each layer

[0083]

[0084] Step S30: Determine the risk levels of the wells where each layer is located according to the comprehensive water influx evaluation indexes of the wells where each layer is located;

[0085] Calculate the comprehensive water influx evaluation index of the wells where each layer is located according to the comprehensive water influx evaluation indexes of the wells where each layer is located R , and then judge the risk level of each layer according to the comprehensive water influx evaluation index R of the wells where each layer is located; among them, the water influx risks of the wells where each layer is located are divided into three levels, R If the value is in the top 30% quantile of all layers, it is identified as a high risk; RIf the value is between 30% and 70% of all horizons, it is identified as medium risk; R If the value is in the lower 30% quantile of all horizons, it is identified as low risk.

[0086] After normalization, map each index value to the interval [0,1] to eliminate the influence of dimension. Establish a linear weighted comprehensive evaluation model, and set the weight coefficient of each index to 1 / 3 to reflect the balanced contribution of each index to the water invasion risk. Therefore, the comprehensive evaluation index of water invasion R The calculation formula is as follows:

[0087]

[0088] In the formula: R is the comprehensive evaluation index of water invasion; is the water invasion volume coefficient; is the advancing speed of the water invasion front; is the water invasion streamline density index;

[0089] Among them, the comprehensive evaluation index of water invasion in the low-permeability layer R is 0.013; the comprehensive evaluation index of water invasion in the medium-permeability layer R is 0.303; the comprehensive evaluation index of water invasion in the high-permeability layer R is 0.593;

[0090] Therefore, the well where the low-permeability layer is located is of low risk, the well where the medium-permeability layer is located is of medium risk, and the well where the high-permeability layer is located is of high risk;

[0091] Step S40: Taking the minimization of the standard deviation of the advancing speed of the water invasion front in each layer as the objective function and the production rates of three production wells as the optimization variables, construct a mathematical model for regulating the water invasion flow field of multiple layers and multiple wells;

[0092] The minimization of the standard deviation of the advancing speed of the water invasion front is defined as:

[0093] (13)

[0094] In the formula: N is the number of reservoirs; is the standard deviation of the advancing speed of the water invasion front; is the k advancing speed of the water invasion front in the layer;

[0095] The optimization variables are the production rates of each well, which are expressed as follows:

[0096] (14)

[0097] In the formula: to are the production rates of the 1st to the production wells respectively.

[0098] The production rates of each well need to satisfy the upper and lower limit constraints of their respective wells:

[0099] (15)

[0100] In the formula: and are respectively the j minimum and maximum production rates of the production well.

[0101] Step S50: In the mathematical model for regulating the water invasion flow field of multi-layer and multi-well, use the adaptive covariance matrix evolution algorithm to iteratively optimize and minimize the standard deviation of the water invasion front advance speed of each layer, and obtain the production rates of each layer.

[0102] First, at the initial stage of the algorithm, construct a virtual training sample library. Combine with a numerical simulator and adopt various enhancement methods such as data interpolation, physical constraint perturbation, and multi-dimensional projection to improve the exploration ability of the adaptive covariance matrix evolution algorithm in the complex objective function space and reduce the risk of falling into local optima. Secondly, introduce a parallel computing framework, allocate the individual fitness evaluation tasks in the population to be executed simultaneously in a multi-core or multi-node environment, significantly reduce the single-round iteration time, and improve the optimization efficiency. The process of the adaptive covariance matrix evolution algorithm is as Figure 5 shown.

[0103] According to the comprehensive evaluation index of water invasion of each well's layer position, implement production restriction and water control for high-risk wells, that is, impose constraints to reduce production in the next time step; optimize the production allocation for medium-risk wells, that is, impose additional constraints and use the algorithm to search for the best production rate; increase production and speed up for low-risk wells, that is, impose constraints to increase production in the next time step. By differentially and automatically regulating the production rates of the well group, dynamically matching the changes in the water invasion flow field, and using the improved adaptive covariance matrix evolution algorithm to iteratively optimize and minimize the standard deviation of the water invasion front advance speed of each layer, the water invasion front after production regulation is as Figure 6 shown.

[0104] As mentioned above, it is not any form of limitation to the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art, without departing from the scope of the technical solution of the present invention, can make some changes or modifications to the above-disclosed technical content to be equivalent change equivalent embodiments. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention all fall within the scope of the technical solution of the present invention.

Claims

1. A method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability tight sandstone gas reservoirs, characterized in that: The following steps are involved: Step S10, simulating the water invasion process of the low permeability layer, the medium permeability layer, and the high permeability layer respectively by a streamline numerical simulation method of a modified Pollock streamline tracing algorithm coupled with gas compressibility, and obtaining water invasion parameters of each layer; The seepage differential equation of the modified Pollock streamline tracing algorithm coupled with gas compressibility is: Where: is the formation permeability: is the viscosity of natural gas; For pressure; is the porosity; t For time; Z is the absolute pressure of the gas; Step S20, calculating the comprehensive evaluation index of water invasion of the wells where each layer is located according to the water invasion parameters of each layer; Step S30, determining the risk level of each layer according to the comprehensive evaluation index of water intrusion of the well where each layer is located; Step S40, constructing a multi-layer and multi-well water intrusion field control mathematical model; Step S50, in the multi-layer and multi-well water invasion flow field control mathematical model, an adaptive covariance matrix evolutionary algorithm is used to iteratively optimize and minimize the standard deviation of the water invasion front advancement speed of each layer, and obtain the production of the wells in each layer.

2. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability dense sandstone gas reservoirs according to claim 1 is characterized in that: The water intrusion comprehensive evaluation index includes water intrusion volume coefficient, water intrusion front advancing speed, and water intrusion streamline density index.

3. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability dense sandstone gas reservoirs according to claim 2 is characterized in that: The calculation formula of the water intrusion volume coefficient is: Where: is the water intrusion volume coefficient; The amount of water intrusion; For time; is the pressure drop; The calculation formula of the water invasion front edge propulsion speed is: Where: is the advancing speed of the water invasion front; The water intrusion front is Advance distance in time; The calculation formula of the water intrusion flow line density index is: Where: is the water intrusion streamline density index; is the number of water intrusion flow lines in this layer; is the total number of streamlines.

4. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability dense sandstone gas reservoirs according to claim 1 is characterized in that: In step S30, the water invasion comprehensive evaluation index of each well in each layer is calculated according to the water invasion comprehensive evaluation index of each well in each layer. R According to the comprehensive evaluation index of water invasion in the wells of each layer R Determine the risk level of the wells in each layer; the water invasion risk of the wells in each layer is divided into three levels: R If the value is in the top 30% quantile of all layers, it is considered high risk; R If the value is between 30% and 70% of all layers, it is considered as medium risk; R Values ​​in the bottom 30% quantile of all layers are considered low risk.

5. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability dense sandstone gas reservoirs according to claim 4 is characterized in that: The water intrusion comprehensive evaluation index R The calculation formula is: Where: R is the comprehensive evaluation index of water intrusion; is the water intrusion volume coefficient; is the advancing speed of the water invasion front; is the water intrusion streamline density index.

6. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability tight sandstone gas reservoirs according to claim 1 is characterized in that: The multi-layer and multi-well water invasion flow field control mathematical model takes minimizing the standard deviation of the water invasion front advancement speed of each layer as the core objective function, takes the production of each layer as the optimization variable, and imposes constraints based on the risk level of each layer.

7. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability tight sandstone gas reservoirs according to claim 6 is characterized in that: The formula for minimizing the standard deviation of the water invasion front velocity of each layer is: Where: N is the number of reservoirs; is the standard deviation of the water invasion front advancing velocity; For the k The advancing speed of the water invasion front of the layer; It is the arithmetic mean of the advancing velocities of the water invasion front in all layers.

8. The method for balanced control of water intrusion field in three-layer horizontal wells of highly heterogeneous low-permeability tight sandstone gas reservoirs according to claim 6 is characterized in that: The constraints in the multi-layer and multi-well water intrusion field control mathematical model are: When the risk level is low risk, the constraint is to increase the production in the next time step; When the risk level is medium risk, the constraint is to impose additional constraints; When the risk level is high, the constraint is to reduce the output in the next time step.

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