A method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function.
By constructing a multi-morphological pressure drop curve function based on the Logistic pressure drop function, the problem of reliance on manual experience and lack of flexibility in the existing technology is solved, realizing the flexibility and efficiency of pressure drop control in coalbed methane wells, and improving the production efficiency and economy of coalbed methane wells.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHINA UNIV OF PETROLEUM (EAST CHINA)
- Filing Date
- 2026-03-16
- Publication Date
- 2026-05-26
AI Technical Summary
Existing methods for controlling pressure drop in coalbed methane wells rely heavily on manual experience, lack flexibility, and are difficult to uniformly express various drainage and production needs. Furthermore, the pressure drop curve is not used as a systematic optimization object, making it difficult to achieve efficient bottom hole pressure regulation.
The method based on the Logistic pressure drop function is adopted. By constructing a normalized Logistic basis function, the multi-morphological pressure drop curve functions are weighted and superimposed, and linearly mapped to the actual pressure range to generate bottom hole flowing pressure curves that meet different target pressure ranges. The optimal pressure drop curve is generated by parameter optimization.
This method improves the flexibility and adaptability of pressure drop curves, enabling the generation of various pressure drop patterns. It solves the problems of reliance on manual experience and limited pattern variety in traditional methods, thereby improving the production efficiency and economy of coalbed methane wells.
Smart Images
Figure CN121835457B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of coalbed methane development, and specifically to a method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function. Background Technology
[0002] Coalbed methane (CBM) well drainage systems and bottom hole flowing pressure control technology are important research directions in the field of CBM development. As CBM development evolves from shallow to deep wells and from vertical wells to horizontal wells and well groups, bottom hole flowing pressure control methods have gradually evolved from simple constant pressure or constant production control to a phased drainage system design centered around the "drainage-desorption-stabilization" process. Existing technologies mainly suffer from the following problems:
[0003] Existing segmented pressure drop control methods heavily rely on manual experience, resulting in highly subjective stage boundaries. The existing "five-stage, three-pressure method" for high-rank coalbed methane wells divides the drainage process into five stages: drainage, pressure buildup, pressure control, stable and high production, and decline. It provides specific operational rules such as the dynamic fluid level descent rate (e.g., 5–7 m / d during the drainage stage), the control range of bottom hole flowing pressure fluctuations (e.g., 0–0.03 MPa), and the control range of gas release (e.g., 200–300 m³). Field application reports show that the average production of a single well in the southern Qinshui Basin increased from 707 m³ / d to 1812 m³ / d. However, stage nodes are typically set manually by engineers based on experience or limited production data, lacking unified standards across different wells and blocks, making the drainage system difficult to replicate and promote.
[0004] Fixed-function pressure drop curves lack flexibility and struggle to adapt to diverse drainage and production needs simultaneously. The core of existing "pressure-controlled drainage gas production methods" is to meet the drainage needs of wellbore disturbances (drilling and completion fluids, coal dust, and coal scrap) with the first day's drainage volume, while simultaneously injecting pressurizing media to maintain a certain daily pressure drop at the bottom of the well, thus preventing pore / fracture retraction and closure. This method emphasizes the concept of "constant daily pressure drop" and does provide engineering solutions for stress-sensitive damage caused by excessively rapid pressure drops. However, its essence remains constrained by a few rules for local processes, making it difficult to express more complex multi-morphological pressure drops (such as L-step-L, slow-fast-slow, etc.) and the coordinated pressure drop distribution between different wells. A single function form can only generate a limited number of pressure drop patterns. When reservoir conditions, drainage objectives, or engineering constraints change, it is often necessary to reselect the function type, lacking a unified modeling framework.
[0005] Existing optimization methods do not systematically optimize the pressure drop curve itself. Current technologies collect actual bottom-hole flowing pressure using bottom-hole sensors, and the control system compares this with preset reference values to adjust the opening of the exhaust / injection control valves, achieving "timely, stable, and reliable" control of the bottom-hole flowing pressure. However, existing technologies rely on dynamic fluid level adjustments, which suffer from lag, difficulty in providing high-frequency and timely feedback, and the risk of coal dust causing pump jamming. In existing studies, bottom-hole flowing pressure is only used in calculations as single-point values or simple time series, failing to systematically design and compare the overall shape of the pressure drop curve.
[0006] Therefore, there is a need for a flexible, non-manual, and uniformly expressible method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function. Summary of the Invention
[0007] The main objective of this invention is to provide a pressure drop control method for coalbed methane wells based on the Logistic pressure drop function, in order to solve the problems of existing segmented pressure drop control methods that are highly dependent on human experience, lack flexibility, and cannot be uniformly expressed.
[0008] To achieve the above objectives, this invention provides a method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function, specifically including the following steps:
[0009] S1 determines the pressure drop boundary conditions, making time dimensionless.
[0010] S2, construct the normalized Logistic basis function to describe the voltage drop characteristics.
[0011] S3 constructs a multimorphic pressure drop curve function by weighting and superimposing several normalized Logistic basis functions.
[0012] S4 linearly maps the multi-mode pressure drop curve function to the actual pressure range to obtain the target bottom hole flowing pressure curve.
[0013] S5 generates different target bottom hole flowing pressure curves that meet the three-stage control requirements of early drainage, mid-term desorption expansion, and late-term stable production depletion in coalbed methane production by changing parameters. The parameters include: the weight of pressure drop events, the steepness of pressure drop events, and the center time of pressure drop events.
[0014] S6. By comparing the bottom-hole flowing pressure curves of different target wells, the optimal pressure drop curve is obtained.
[0015] Furthermore, step S1 specifically includes the following steps:
[0016] S1.1 Obtain the basic pressure boundary and time scale of the well or well group to be optimized, including: initial bottomhole flowing pressure or initial reservoir pressure. Ultimate bottom hole flowing pressure and total optimization cycle time .
[0017] S1.2, make time dimensionless to τ, so that the domain of the pressure drop curve is fixed at [0,1]:
[0018] , ;
[0019] in, For production time, It is dimensionless time.
[0020] Further, step S2 specifically involves: performing endpoint normalization on the Logistic function so that the Logistic function... When the time is 0, in Time 1:
[0021] ;
[0022] ;
[0023] in, For steepness parameter, At the central moment, For steepness, For the Logistic function, The normalized basis functions satisfy... =0, And for Monotonically increasing, It is a natural exponential function.
[0024] Furthermore, the multi-mode pressure drop curve function in step S3 for:
[0025] ;
[0026] ;
[0027] in, To reduce the total number of incidents, For the first The weights of each pressure drop event satisfy: pressure difference , For the first The steepness of a pressure drop event, For the first The central moment of a pressure drop event.
[0028] Furthermore, step S4 specifically includes:
[0029] Linearly map the multi-morphic pressure drop curve function to the actual pressure range. The target wellbore bottom flowing pressure curve is obtained:
[0030] ;
[0031] in, For the target bottom hole flowing pressure, As the initial pressure, This represents the final ultimate pressure.
[0032] Furthermore, step S5 specifically includes the following steps:
[0033] S5.1, desorption pressure Mapped to :
[0034] .
[0035] S5.2, Solve for the time to reach the desorption pressure. This serves as a node check value for the end of early drainage or the start of desorption expansion:
[0036] ;
[0037] when hour, It can be directly obtained from the inverse function of the normalized logistic function; when When solving using single-variable numerical root finding within the range [0,1], .
[0038] S5.3 uses empirical initialization or machine learning to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the bottom-hole flowing pressure curves for different targets.
[0039] Furthermore, in step S5.3, the weights, steepness, and center moments of the optimal pressure drop event are obtained using empirical initialization, thus yielding the specific bottom-hole flowing pressure curves for different targets:
[0040] Based on the well group's desorption pressure, drainage capacity, stress sensitivity risk, and surface system capacity, first determine , and then give Subsequently through The pressure differential share is allocated during the distribution phase and finally passed through... The degree of pressure drop during the adjustment phase generates a pressure drop curve.
[0041] Furthermore, in step S5.3, machine learning is used to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the specific bottom-hole flowing pressure curves for different targets:
[0042] parameter set As optimization variables, driven by numerical simulation of a single well or well group, with cumulative gas production or net present value as the objective function, constraints such as bottomhole flowing pressure limit, maximum pressure drop rate, fluid production capacity, total well group production, and surface processing capacity are applied. The optimal parameters are solved using methods such as genetic algorithm, particle swarm optimization, or reinforcement learning. The parameters of the target bottom hole flowing pressure function are cyclically set to obtain different target bottom hole flowing pressure curves.
[0043] The present invention has the following beneficial effects:
[0044] This invention avoids the problem of manually defining stages by introducing a family of continuously parameterized voltage drop functions, allowing stage characteristics to be naturally reflected through function parameters.
[0045] This invention generates various voltage drop patterns, such as L-shaped, inverse L-shaped, linear, and step-shaped, under the same mathematical structure by weighted superposition of multiple Logistic functions, which significantly improves the adaptability of the model.
[0046] This invention introduces the pressure drop curve parameters as complete decision variables into the optimization process, fundamentally solving the problem of "curves that cannot be optimized". Attached Figure Description
[0047] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:
[0048] Figure 1 A flowchart of a pressure drop control method for coalbed methane wells based on the Logistic pressure drop function of the present invention is shown.
[0049] Figure 2 Typical pressure drop curves for a species obtained using the method provided in this invention are shown.
[0050] Figure 3 A schematic diagram of daily gas production corresponding to different pressure drop curves is shown.
[0051] Figure 4 A schematic diagram showing the daily water production corresponding to different pressure drop curves is presented. Detailed Implementation
[0052] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0053] like Figure 1 The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function, as shown, specifically includes the following steps:
[0054] S1 determines the pressure drop boundary conditions, making time dimensionless.
[0055] S2, construct the normalized Logistic basis function to describe the voltage drop characteristics.
[0056] S3 constructs a multimorphic pressure drop curve function by weighting and superimposing several normalized Logistic basis functions.
[0057] S4 linearly maps the multi-mode pressure drop curve function to the actual pressure range to obtain the target bottom hole flowing pressure curve.
[0058] S5 generates different target bottom hole flowing pressure curves that meet the three-stage control requirements of early drainage, mid-term desorption expansion, and late-term stable production depletion in coalbed methane production by changing parameters. The parameters include: the weight of pressure drop events, the steepness of pressure drop events, and the center time of pressure drop events.
[0059] S6. By comparing the bottom-hole flowing pressure curves of different target wells, the optimal pressure drop curve is obtained.
[0060] Specifically, step S1 includes the following steps:
[0061] S1.1 Obtain the basic pressure boundary and time scale of the well or well group to be optimized, including: initial bottomhole flowing pressure or initial reservoir pressure. Ultimate bottom hole flowing pressure (Minimum safe pressure or economic limit pressure of the wellbore can be taken) and total optimization cycle time. .
[0062] S1.2, To make the pressure drop curve more universal, the time is dimensionless and τ is used, fixing the domain of the pressure drop curve to [0,1], which facilitates cross-well comparison and parameter migration:
[0063] , ;
[0064] in, Production time (days) It is dimensionless time.
[0065] Specifically, step S2 is as follows:
[0066] To describe the time distribution characteristics of pressure drop features (i.e., a significant increase in the pressure drop rate and the release of a certain pressure difference within a certain time window), this invention uses the Logistic function as the basis function. The Logistic function is monotonic, smooth, and differentiable, with its center time... Controlling the timing of pressure drop events and steepness The "speed" of the voltage drop event (i.e., the peak value and duration of the voltage drop rate) is controlled. To ensure consistency of the function at the boundaries under different parameters and to achieve strict endpoint constraints, the endpoints of the Logistic function are normalized to ensure that the Logistic function... When the time is 0, in Time 1:
[0067] ;
[0068] ;
[0069] in, For steepness parameter, At the central moment, For steepness, The larger the pressure drop, the more concentrated and steeper the pressure drop. For the Logistic function, The normalized basis functions satisfy... =0, And for Monotonically increasing, It is a natural exponential function. ∈(0,1) represents the center time parameter, the "time position" where the pressure drop event occurs; for example... =0.1 indicates that the main pressure drop is concentrated in the first 10% of the total cycle. This indicates the percentage of a single pressure drop event that has been completed. near The period of fastest growth corresponds to the most concentrated release of pressure from this event.
[0070] The physical meaning of this basis function is: when near hour, The fastest growth corresponds to the most concentrated release of pressure reduction; when keep away hour, The growth is slow, corresponding to a relatively small pressure drop rate.
[0071] Specifically, to achieve a unified expression of various voltage drop modes, this invention weighted and superimposed several normalized Logistic basis functions to obtain a multi-mode voltage drop curve function. Its engineering significance is: to convert the "change of bottom hole flowing pressure over time" into the "total pressure difference (…)". - "The proportion that has been released" thus decouples the shape control from the pressure amplitude.
[0072] Indicates dimensionless time Below, the proportion of the total pressure differential that has been released. Weighting The "share" of pressure differential released in each pressure drop event is determined, thus forming different pressure drop patterns and phase allocations.
[0073] Step S3 Multimorphic pressure drop curve function for:
[0074] ;
[0075] ;
[0076] in, To reduce the total number of incidents, For the first The weights of each pressure drop event satisfy: pressure difference , For the first The steepness of a pressure drop event, For the first The central moment of each pressure drop event. This can be obtained from the normalization property. , . The number of pressure drop events represents the number of "pressure control actions / pressure drop phase events" included in the corresponding pressure drop curve; =1 represents a single-event curve. =2 can produce composite morphologies such as step / double-peak rates.
[0077] The function of the multi-mode pressure drop curve is to uniformly map the complex multi-stage pressure drop process into a curve representing the change in the pressure difference release ratio over time; by adjusting... It can generate different pressure drop patterns and ensure that the endpoints strictly meet the design pressure boundaries.
[0078] Specifically, step S4 is as follows:
[0079] Linearly map the multi-morphic pressure drop curve function to the actual pressure range. The target wellbore bottom flowing pressure curve is obtained:
[0080] ;
[0081] in, The target bottom hole flowing pressure (MPa) is used. The initial pressure is (MPa). The final ultimate pressure (MPa); by , It can be known that: , This ensures that the endpoints of the target curve meet engineering constraints.
[0082] This is the "target curve" used for on-site pressure control in this invention, and it is also the core object of optimization and evaluation.
[0083] The significance of this mapping lies in the fact that the shape of the pressure drop curve changes from... The decision is made based on the pressure amplitude. and The decision to decouple the two allows curves with the same shape to be quickly transferred to the pressure range of different wells.
[0084] Specifically, step S5 includes the following steps:
[0085] S5.1, desorption pressure Mapped to :
[0086] .
[0087] S5.2, Solve for the time to reach the desorption pressure. This serves as a node check value for the end of early drainage or the start of desorption expansion:
[0088] ;
[0089] when hour, It can be directly obtained from the inverse function of the normalized logistic function; when When this is the case, a single-variable numerical solution (such as the bisection method) can be used to solve the problem within the range [0,1]. By adjusting make Located within the expected range, it can achieve consistency between the stage significance and the curve shape.
[0090] To explicitly represent the starting point of the coalbed methane desorption stage in the curve design, the desorption pressure will be reached. Time As a key node, the desorption pressure is first mapped to the cumulative pressure drop ratio. Its physical meaning is: under the total pressure difference ( - From ) Down to The proportion.
[0091] S5.3 uses empirical initialization or machine learning to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the bottom-hole flowing pressure curves for different targets.
[0092] Specifically, in step S5.3, the weights, steepness, and center moments of the optimal pressure drop event are obtained using empirical initialization, thereby yielding the bottom-hole flowing pressure curves for different targets:
[0093] Based on the well group's desorption pressure, drainage capacity, stress sensitivity risk, and surface system capacity, first determine (Usually 2 or 3), then given (Corresponding to the main pressure drop periods in each stage), then through The pressure differential share is allocated during the distribution phase and finally passed through... The degree of pressure drop within the adjustment phase generates different target bottom hole flowing pressure curves.
[0094] This invention changes parameters Different pressure drop patterns are generated to meet the three-stage control requirements of coalbed methane drainage: "early drainage—mid-term desorption and expansion—late-term stable production depletion." Its usage is as follows:
[0095] When M=1, it is a single-event voltage drop curve. This determines whether the curve is close to linear or exhibits a clear L-shaped / inverse L-shaped trend; Determine whether the main pressure drop occurs in the early or late stages. The L-shaped pressure drop curve is suitable for the rapid pressure drop phase during drainage. ∈[0.05, 0.20], ∈[10, 30], =1. The inverse L-shaped voltage drop curve shows that the voltage stabilizes first, then drops: ∈[0.7, 0.9], ∈[10, 30], =1. A linear pressure drop curve exhibits an approximately linear change throughout the entire production cycle, making it suitable for the drainage stage where a stable pressure drop rate is required. ∈[0.4, 0.6], ∈[2, 5], =1.
[0096] When M=2 or M=3, it is a multi-event pressure drop curve, which can form a combination of stepped and S-shaped patterns. At this time, the weight... Used to allocate the differential pressure share at each stage; center time Used to determine the timing of pressure drop events at different stages; steepness Used to control whether the internal pressure drop is "concentrated" and "rapid". For example, a stepped pressure drop curve is suitable for the rapid pressure drop phase during drainage. ∈[0.40,0.60], ∈[0.15,0.30], ∈[3,8]; ∈[0.40,0.60], ∈[0.50,0.65], ∈[8,18]; and ∈[0.25,0.45]. The S-order pressure drop curve shows an initial stabilization followed by a pressure drop: ∈[0.35,0.55], ∈[0.05,0.15], ∈[15,40]; ∈[0.45,0.65], ∈[0.75,0.90], ∈[15,40]; and ≥0.60.
[0097] Specifically, in step S5.3, machine learning is used to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the bottom-hole flowing pressure curves for different targets as follows:
[0098] parameter set As optimization variables, driven by numerical simulation (or machine learning surrogate model) of a single well or well group, with cumulative gas production or net present value as the objective function, constraints such as bottomhole flowing pressure limit, maximum pressure drop rate, fluid production capacity, total well group production, and surface processing capacity are applied. The optimal parameters are solved using methods such as genetic algorithm, particle swarm optimization, or reinforcement learning. The parameters of the target bottom hole flowing pressure function are cyclically set to obtain different target bottom hole flowing pressure curves.
[0099] In field applications, As the target trajectory of the pressure control system, it is tracked and controlled in conjunction with real-time monitoring data: by adjusting the pumping frequency, throttle valve opening or wellhead pressure setting, the actual bottom hole flowing pressure is made close to the target curve; and the parameters can be recalibrated according to a preset cycle to achieve closed-loop optimization.
[0100] The method provided by this invention will be described in detail below, taking into account actual mining conditions:
[0101] For the design of pressure drop drainage system in deep coalbed methane horizontal wells, the initial pressure and control boundary are set as: reservoir pressure (or initial bottomhole flowing pressure). =7MPa, desorption pressure =4MPa, ultimate bottom hole flowing pressure =1.01MPa. To facilitate demonstration of the entire curve design process, the control period is taken as... =1825d (5 years). This invention constructs a normalized Logistic basis function and performs weighted superposition to form a multi-morphological pressure drop curve function. Then, the bottom hole flowing pressure target curve is obtained by mapping. Following the process of "morphology - parameter range - parameter instantiation - desorption node verification", five typical pressure drop schemes were obtained: L-shaped, inverse L-shaped, linear, step, and S-shaped.
[0102] Using desorption pressure as the stage node check quantity, calculate and :
[0103] ;
[0104] Substituting the operating conditions of this embodiment =7, =4MPa, =1.01MPa:
[0105] ;
[0106] The time to reach the desorption pressure is then obtained by solving the following formula. It can be used as a node check value for "end of early drainage / beginning of desorption expansion".
[0107] ;
[0108] When M=1, the above formula can be obtained directly from the inverse function of the normalized Logistic function; when M≥2, a single-variable numerical solution (such as the bisection method) is used to solve the problem in the range [0,1]. ,Right now In this embodiment, the bisection method is used for the case where M=2, and the convergence tolerance is taken as 10−6.
[0109] Five voltage drop schemes are obtained according to the method of the present invention:
[0110] All five of the following schemes satisfy the unified boundary conditions. =7MPa =1.01MPa. Each scheme gives... Its engineering significance (proportion of pressure drop events, degree of pressure drop concentration, and time of occurrence), and the desorption arrival time are given. .
[0111] Option 1: L-type voltage drop scheme (single event) =1).
[0112] This scheme is used to generate an L-shaped morphology of "early rapid pressure reduction," which quickly releases the main pressure differential in the early stage of drainage, allowing the bottom hole flowing pressure to cross the desorption pressure earlier and enter the desorption expansion stage as soon as possible. This embodiment uses: =1, =1.0, =0.20, =20. Among them, =0.20 corresponds to the peak center time of the pressure drop rate. = 365d indicates that the period of fastest pressure drop occurs within approximately one year after production begins; =20 indicates a higher degree of pressure drop concentration (a steeper pressure drop). The time to reach the desorption pressure is determined by... The results obtained in this embodiment are as follows: =368.58d, =0.20196.
[0113] Option 2: Reverse L-shaped voltage drop scheme (single event) =1).
[0114] This scheme is used to generate an inverted L-shaped wellbore with a "slow initial release followed by a concentrated pressure drop" pattern. A higher bottomhole flowing pressure is maintained in the early stages (e.g., to control coal seam damage risk, control sand / coal production, or due to surface system limitations), and the pressure differential is released in a concentrated manner in the later stages. This embodiment uses: =1, =1.0, =0.80, =20. Among them, =0.80 corresponds =1460d, indicating that the major pressure drop event was delayed until a later stage; =20 results in a more concentrated pressure drop in the later stages. The desorption arrival time was calculated as follows: =1457.02d, =0.79837. This result indicates that the desorption pressure is reached relatively late under this scheme, which belongs to the "delayed desorption" strategy. It can be comprehensively weighed with indicators such as yield, moisture content, and coal body stability during optimization.
[0115] Option 3: Linear voltage drop scheme (single event) =1).
[0116] This scheme is used to generate an approximately linear voltage drop profile. Its engineering significance is that the voltage drop rate remains relatively uniform throughout the entire cycle, facilitating on-site pressure control and reducing sensitivity to system fluctuations. This embodiment uses: =1, =1.0, =0.50, =3.5. Among them, =0.50 corresponds =912.5d, the curve is generally symmetrical and there are no obvious "concentrated pressure drop events"); =3.5 makes the curve approximate a straight line. The desorption arrival time is calculated as follows: =913.73d, =0.50067.
[0117] Option 4: S-type voltage drop scheme (two-event, =2).
[0118] This scheme generates a "fast-slow-fast" S-shaped pressure drop pattern, characterized by an early rapid pressure drop across the desorption pressure, a relatively long "plateau" (low pressure drop rate) in the middle stage, and a subsequent rapid pressure drop to the ultimate pressure. Its engineering significance is that it achieves a "double-peak pressure drop rate" through two pressure drop events, satisfying the pressure control logic of "early drainage pressure reduction—middle-stage pressure stabilization / control—late-stage pressure reduction." This scheme adopts... =2 and ≪ And set two events with relatively large steepness to form a clear plateau. Weights The engineering significance is the differential pressure share: .
[0119] The parameters used in this embodiment are: =2;( , = (0.65, 0.35); , ) = (0.10, 30); , ) = (0.88, 25). The corresponding event center time is =182.5d、 =1606d. The pressure differential shares borne by the two events are as follows: =5.99 × 0.65 = 3.8935 MPa; =5.99 × 0.35 = 2.0965 MPa. Event 1 accounts for approximately 65% of the total pressure difference, ensuring sufficient pressure reduction capacity to overcome the desorption pressure in the early stages; Event 2 accounts for the remaining approximately 35% of the total pressure difference, used to further pull the pressure to its limit in the later stages, forming a "final pressure reduction". Desorption arrival time: =259.99d, =0.14246.
[0120] Option 5: Step-type voltage drop scheme (two-event, =2).
[0121] This scheme is used to generate a "slow-fast-slow" step-like pressure drop pattern, meaning a relatively slow pressure drop in the early stage, a significant acceleration in pressure drop in the middle stage (corresponding to enhanced desorption expansion), and a gradual slowdown in pressure drop towards the ultimate pressure in the later stage. Its engineering significance is: controlling the pressure drop rate in the early stage (reducing the risk of coal seam damage / facilitating stable discharge), enhancing pressure drop in the middle stage to drive desorption expansion and increased production, and then gradually controlling depletion in the final stage. This embodiment adopts... =2, setting event 1 with lower kurtosis for "slow" and event 2 with higher kurtosis for "fast", and controlling the pressure difference share between the two events through weights. The parameters are: =2;( , = (0.55, 0.45); , ) = (0.15, 3); , ) = (0.40, 12). The corresponding center time is =273.75d、 =730d. The pressure differential share borne by the two events is: =3.2945MPa; =2.6955 MPa. Desorption arrival time: =713.25d, =0.39082.
[0122] Through the above steps, this invention obtains five parameterizable pressure drop curve schemes under the same boundary conditions, and each curve can be directly derived from a set of parameters. When used in the field or in simulation, the pressure drop curve of this invention can be obtained based on different parameters and used as the target trajectory for numerical simulation (constant pressure control) or pressure control system.
[0123] This invention changes parameters Generate different voltage drop patterns, such as Figure 2 As shown, the pressure drop pattern affects coalbed methane production. Figure 3 and Figure 4 The daily gas and water production corresponding to different pressure drop curves are shown. Based on this pressure drop function, we can reveal the impact of different pressure drop schemes on production by adjusting parameters, and identify the optimal pressure drop scheme. Among the five schemes mentioned above, the L-shaped pressure drop pattern has a longer stable production time and a higher gas production, making it the optimal scheme.
[0124] This invention addresses the problems of existing coalbed methane drainage systems, such as bottomhole flowing pressure drop curves relying on experience, having a single shape, and being difficult to deeply couple with numerical simulation and intelligent optimization methods. It proposes a coalbed methane well pressure drop optimization method based on a family of multiple Logistic pressure drop functions. By introducing normalized time and parameterized pressure drop functions, the change in bottomhole flowing pressure over time is uniformly represented as an analytical curve controlled by a small number of parameters, achieving quantitative description and adjustable design of the pressure drop curve shape. Compared with traditional drainage systems that use piecewise straight lines, fixed L-shaped curves, or manually divided stages, the technical solution of this invention can generate various typical pressure drop shapes, such as L-shaped, inverse L-shaped, straight, and stepped curves, by adjusting the weights, occurrence times, and steepness parameters of pressure drop events, while ensuring strict satisfaction of bottomhole flowing pressure boundary conditions. This provides more flexible and refined pressure drop control methods for different coal seam conditions, different well types, and different development stages.
[0125] This invention uses the pressure drop function parameter set as an optimization variable and introduces numerical simulation or machine learning surrogate models for solution, transforming the bottomhole flowing pressure curve from an "empirical given quantity" into an "optimizable decision variable." Through constraint verification of desorption pressure corresponding to time nodes, a quantitative correspondence between the pressure drop curve and the physical process of coalbed methane—"early drainage—mid-term desorption expansion—late-term stable production decline"—is achieved, thus avoiding the problems of strong subjectivity and difficulty in unifying traditional stage divisions. This method can not only effectively control coal body damage and sand production risks caused by excessively rapid pressure drop in the early stage, but also improve the desorption driving force by reasonably enhancing the pressure drop rate in the desorption expansion stage, and achieve gradual decline control in the later stable production stage. Overall, it is beneficial to improve the cumulative gas production and development economy of single coalbed methane wells and well groups. Simultaneously, because the pressure drop curve has an analytical expression, it is easy to call and track execution in real time in the surface pressure control system, thereby significantly improving the engineering operability and intelligence level of drainage and production system design and implementation.
[0126] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.
Claims
1. A method for controlling pressure drop in a coalbed methane well based on a logistic pressure drop function, characterized by, Specifically, the steps include the following: S1, determine the pressure drop boundary conditions, and make time dimensionless; S2, construct the normalized Logistic basis function to describe the voltage drop characteristics; S3, which involves weighted superposition of several normalized Logistic basis functions to construct a multi-morphological pressure drop curve function; S4, linearly map the multi-mode pressure drop curve function to the actual pressure range to obtain the target bottom hole flowing pressure curve; S5 generates different target bottom hole flowing pressure curves that meet the three-stage control requirements of early drainage, mid-term desorption expansion, and late-term stable production depletion in coalbed methane production by changing parameters. The parameters include: the weight of pressure drop events, the steepness of pressure drop events, and the center time of pressure drop events. S6. By comparing the bottom-hole flowing pressure curves of different target wells, the optimal pressure drop curve is obtained.
2. The method according to claim 1, wherein, Step S1 specifically includes the following steps: S1.1, obtaining the base pressure boundary and time scale of the well or well group to be optimized, including: initial bottom-hole flowing pressure or initial reservoir pressure , final limit bottom-hole flowing pressure , and total length of optimization period ; S1.2, make time dimensionless to τ, so that the domain of the pressure drop curve is fixed at [0,1]: ， ； wherein, tprod is the production time, tnon-dim is the non-dimensional time.
3. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 1, characterized in that, Step S2 is specifically: endpoint normalization is performed on the Logistic function, so that the Logistic function takes 0 at and takes 1 at . ； ； in, For steepness parameter, At the central moment, For steepness, For the Logistic function, The normalized basis functions satisfy... =0, And for Monotonically increasing, It is a natural exponential function.
4. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 1, characterized in that, Step S3 Multimorphic pressure drop curve function for: ； ； in, To reduce the total number of incidents, For the first The weights of each pressure drop event satisfy: pressure difference , For the first The steepness of a pressure drop event, For the first The central moment of a pressure drop event.
5. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 1, characterized in that, Step S4 is as follows: Linearly map the multi-morphic pressure drop curve function to the actual pressure range. The target wellbore bottom flowing pressure curve is obtained: ； in, For the target bottom hole flowing pressure, As the initial pressure, This represents the final ultimate pressure.
6. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 1, characterized in that, Step S5 specifically includes the following steps: S5.1, desorption pressure Mapped to : ； S5.2, Solve for the time to reach the desorption pressure. This serves as a node check value for the end of early drainage or the start of desorption expansion: ； when hour, It can be directly obtained from the inverse function of the normalized logistic function; when When solving using single-variable numerical root finding within the range [0,1], ; S5.3 uses empirical initialization or machine learning to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the bottom-hole flowing pressure curves for different targets.
7. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 6, characterized in that, In step S5.3, the weights, steepness, and center moments of the optimal pressure drop event are obtained using empirical initialization, leading to the specific bottom-hole flowing pressure curves for different targets: Based on the well group's desorption pressure, drainage capacity, stress sensitivity risk, and surface system capacity, first determine , and then give Subsequently through The pressure differential share is allocated during the distribution phase and finally passed through... The degree of pressure drop within the adjustment phase generates different target bottom hole flowing pressure curves.
8. The method for controlling pressure drop in coalbed methane wells based on the Logistic pressure drop function according to claim 6, characterized in that, In step S5.3, machine learning is used to obtain the weight of the optimal pressure drop event, the steepness of the pressure drop event, and the center time of the pressure drop event, thereby obtaining the specific bottom-hole flowing pressure curves for different targets: parameter set As optimization variables, driven by numerical simulation of a single well or well group, with cumulative gas production or net present value as the objective function, constraints are applied including bottomhole flowing pressure limit, maximum pressure drop rate, fluid production capacity, total well group production, and surface processing capacity. The optimal parameters are then solved using genetic algorithms, particle swarm optimization, or reinforcement learning methods. The parameters of the target bottom hole flowing pressure function are cyclically set to obtain different target bottom hole flowing pressure curves.