A quantitative judgment method for drainage gas recovery implementation time selection of low-permeability gas well

Abstract

The application provides a quantitative judgment method for sorting implementation time of low-permeability gas well drainage gas recovery, and the specific steps are as follows: step one, according to daily water production q w and daily gas production q g of the wellhead of the gas well, cumulative water production W and cumulative gas production G of the gas well in a required number of days are calculated; step two, according to the cumulative water production W and the cumulative gas production G obtained in step one, cumulative water-gas ratio F is obtained, and a curve of the cumulative water-gas ratio changing with the number of production days is drawn; when the curve shows an increasing phenomenon, a corresponding increasing mathematical model is established; step three, according to the determined increasing mathematical model, a prediction function of water-out probability of the gas well is established, and different urgency time divisions for implementing the drainage gas recovery measures are determined. The application does not require oil and casing pressure data of the gas well, only requires daily water production and daily gas production data, reduces the requirement of the gas well production process, has universal applicability, reduces the lag of the drainage gas recovery measures, and is helpful to improve the implementation effect of the drainage gas recovery.

Description

Technical Field

[0001] This invention relates to the field of natural gas development, and in particular to a quantitative method for determining the timing of drainage and gas production in low-permeability gas wells. Background Technology

[0002] Gas wells are affected by water production, resulting in severe problems such as rapid decline, short life cycle, and even rapid flooding. These issues severely restrict the production capacity of gas wells and ultimately lead to a decrease in cumulative gas production.

[0003] To achieve efficient gas field development and long-term stable production, accurately predicting the liquid accumulation trend in gas wells is crucial. Therefore, establishing a method for selecting the timing of drainage and gas production is one of the important methods for controlling water production in gas wells. However, current methods for determining the timing of drainage and gas production rely on simple statistical methods based on the fact that severe wellbore liquid accumulation has led to large oil-casing pressure differentials, decreased daily gas production, and increased water-gas ratios. These methods lack early warning capabilities for water-producing gas wells and either blindly implement drainage and gas production measures regardless of water production, resulting in high production costs and poor drainage and gas production effects. This method is a simple statistical analysis based on data after significant liquid accumulation has occurred, making it difficult to standardize characteristic parameters for different gas wells and lacking accuracy in evaluation. Furthermore, it has high requirements for gas well production processes (e.g., it is not applicable to wells without casing), limiting its applicability. Currently, there is no widely applicable, rapid, and quantitative method for determining the timing of drainage and gas production in gas wells. Summary of the Invention

[0004] To overcome the problems of blind implementation, high requirements for gas well production processes (including the need for casing pressure), reliance on simple statistical analysis methods based on severe fluid accumulation, lack of early warning, delayed drainage and gas production measures, inconsistent standards, and low accuracy in existing drainage and gas production processes, this invention provides a quantitative judgment method for selecting the timing of drainage and gas production in low-permeability gas wells. This invention establishes a mathematical model for selecting the timing of drainage and gas production by analyzing the changing patterns of gas well production data. This invention does not require gas well oil or casing pressure data, only daily water and gas production data, reducing the requirements for gas well production processes, possessing universal applicability, reducing the lag in drainage and gas production measures, and helping to improve the effectiveness of drainage and gas production.

[0005] The technical solution adopted in this invention is as follows:

[0006] A quantitative method for determining the timing of drainage and gas production in low-permeability gas wells, comprising the following steps:

[0007] Step 1: Based on the daily water production q at the gas wellhead w and daily gas production q g Calculate the cumulative water production W and cumulative gas production G of the gas well within the required number of days;

[0008] Step 2: Based on the cumulative water production W and cumulative gas production G obtained in Step 1, obtain the cumulative water-gas ratio F, and plot the curve of the cumulative water-gas ratio as a function of production days; when the curve shows an increasing phenomenon, establish the corresponding increasing mathematical model.

[0009] Step 3: Based on the established incremental mathematical model, establish a prediction function for the probability of water flooding in gas wells, and determine the different urgent timings for implementing drainage and gas production measures.

[0010] In step one,

[0011] Cumulative gas production:

[0012] Cumulative water production:

[0013] In the above formula, t represents the number of days.

[0014] In step two, the cumulative water-to-gas ratio F is the cumulative water production / cumulative gas production.

[0015] Cumulative water-air ratio:

[0016] In step two, the increasing model of the cumulative water-gas ratio F during its increasing period is an exponential function:

[0017]

[0018] In the formula, T is the increment period; K is the maximum cumulative water-gas ratio after the gas well is shut down by water flooding; and t is the time, in days.

[0019] In step two, the control parameters T and K are obtained using the least squares method, thereby determining the water-gas ratio increasing model for the water-producing gas well.

[0020] When using the least squares method to find the control parameters of the exponential function, the exponential function is first linearized, and the differential equation of the exponential function is solved. Then, the differential equation is transformed into the corresponding difference equation, and then into a linearized equation. Finally, the control parameters T and K of the increasing model are solved by the least squares method.

[0021] In step three,

[0022] The prediction function for the probability of water flooding in gas wells is:

[0023]

[0024] In the formula, T is the incrementing period, F is the cumulative water-gas ratio, and K is the maximum cumulative water-gas ratio after the gas well is shut in after being flooded.

[0025] When the growth rate reaches the initial stage, the risk of water flooding and shutting down the gas well is low, which is the first stage of drainage and gas production, and no measures are required. When the growth rate reaches the middle stage, the risk of water flooding and shutting down the well is moderate, which is the second stage of drainage and gas production, and necessary drainage and gas production measures are taken according to the situation. When the growth rate reaches the late stage, the risk of water flooding and shutting down the well is very high, which is the third stage of drainage and gas production, and drainage and gas production measures must be taken.

[0026] The initial stage of the increase is m(1T) < 0.63, the middle stage of the increase is 0.63 ≤ m(2T) ≤ 0.86, and the late stage of the increase is 0.86 < m(3T) ≤ 0.95.

[0027] The initial stage of the increase is within the first period T; the middle stage of the increase is within the second period 2T; and the late stage of the increase is within the third period 3T.

[0028] The beneficial effects of this invention are as follows:

[0029] This invention establishes a mathematical model for selecting the timing of gas well drainage and gas production by analyzing the changing patterns of gas well production data. This invention does not require gas well oil or casing pressure data, only daily water and gas production data, thus reducing the requirements for gas well production processes, possessing universal applicability, reducing the lag in drainage and gas production measures, and helping to improve the effectiveness of drainage and gas production.

[0030] This invention enables timely detection of water flooding trends in gas wells, advance planning of drainage and gas production measures, and scientific implementation of corresponding drainage and gas production measures in the early, middle, and late stages of increasing water-to-gas ratio, thereby improving the efficiency of drainage and gas production implementation.

[0031] The following will provide further explanation in conjunction with the accompanying drawings. Attached Figure Description

[0032] Figure 1 This is a comparison chart of the daily water-to-gas ratio and the cumulative water-to-gas ratio of a gas well.

[0033] Figure 2 This is a comparison chart of the actual water-gas ratio of the gas well and the prediction results of the water-gas ratio index model for that well.

[0034] Figure 3 A schematic diagram illustrating the timing of drainage and gas extraction.

[0035] Figure 4 This is a comparison chart showing the cumulative water-to-gas ratio changes and water flooding probability of gas wells after drainage and gas production measures were implemented according to the timing selection method for wells to be judged. Detailed Implementation

[0036] Example 1:

[0037] To overcome the problems of blind implementation, high requirements for gas well production processes (including the need for casing pressure), reliance on simple statistical analysis methods based on severe fluid accumulation, lack of early warning, delayed drainage and gas production measures, inconsistent standards, and low accuracy in existing drainage and gas production processes, this invention provides a quantitative judgment method for selecting the timing of drainage and gas production in low-permeability gas wells. This invention establishes a mathematical model for selecting the timing of drainage and gas production by analyzing the changing patterns of gas well production data. This invention does not require gas well oil or casing pressure data, only daily water and gas production data, reducing the requirements for gas well production processes, possessing universal applicability, reducing the lag in drainage and gas production measures, and helping to improve the effectiveness of drainage and gas production.

[0038] A quantitative method for determining the timing of drainage and gas production in low-permeability gas wells, comprising the following steps:

[0039] Step 1: Based on the daily water production q at the gas wellhead w and daily gas production q g Calculate the cumulative water production W and cumulative gas production G of the gas well within the required number of days;

[0040] Step 2: Based on the cumulative water production W and cumulative gas production G obtained in Step 1, obtain the cumulative water-gas ratio F, and plot the curve of the cumulative water-gas ratio as a function of production days; when the curve shows an increasing phenomenon, establish the corresponding increasing mathematical model.

[0041] Step 3: Based on the established incremental mathematical model, establish a prediction function for the probability of water flooding in gas wells, and determine the different urgent timings for implementing drainage and gas production measures.

[0042] This invention obtains cumulative water-to-gas ratio data from gas wells at different times, and then uses mathematical methods to fit the T and K values ​​of a water-to-gas ratio index model. This allows for the determination of the prediction function m for different time periods, i.e., the probability of flooding (the current cumulative water-to-gas ratio represents the final flooding ratio). The probability of flooding is then divided into three stages: (0-0.63 for the early stage), (0.63-0.85 for the middle stage), and (0.85-0.96 for the late stage). This determines the current stage of the gas well and the urgency of implementing drainage and gas recovery measures.

[0043] The above method can reduce the problems of blindness (blindly carrying out drainage and gas production measures regardless of the water production status of the gas well), complexity (requiring oil casing production technology), lag (relying on data changes after severe liquid accumulation has occurred), low accuracy (simple data change statistics), and difficulty in establishing a unified standard in the implementation process of existing drainage and gas production measures. The gas well water flooding probability prediction function established in this invention divides the different urgent times for implementing drainage and gas production measures, and carries out drainage and gas production measures in a timely manner, thereby improving the implementation effect of drainage and gas production.

[0044] This invention does not require data on gas well oil and casing pressure, but only data on daily water and gas production. It reduces the requirements for gas well production processes, has universal applicability, and can identify the "low, medium, and high" critical times for gas well drainage and gas production. This reduces the lag in drainage and gas production measures and helps improve the effectiveness of drainage and gas production.

[0045] Example 2:

[0046] Based on Embodiment 1, in this embodiment, preferably, in step one,

[0047] Cumulative gas production:

[0048] Cumulative water production:

[0049] In the above formula, t represents the number of days.

[0050] Preferably, in step two, the cumulative water-to-gas ratio F is the cumulative water production / cumulative gas production.

[0051] Cumulative water-air ratio:

[0052] Preferably, in step two, the increasing model of the cumulative water-to-gas ratio F during the increasing period is an exponential function:

[0053]

[0054] In the formula, T is the increment period; K is the maximum cumulative water-gas ratio after the gas well is shut down by water flooding; and t is the time, in days.

[0055] Preferably, in step two, the control parameters T and K are obtained by the least squares method, thereby determining the water-gas ratio increasing model of the water-gas well.

[0056] Preferably, when using the least squares method to find the control parameters of the exponential function, the exponential function is first linearized, the differential equation of the exponential function is solved, the differential equation is then transformed into the corresponding difference equation, and then into a linearized equation. Finally, the control parameters T and K of the increasing model are solved using the least squares method.

[0057] Preferably, in step three,

[0058] The prediction function for the probability of water flooding in gas wells is:

[0059]

[0060] In the formula, T is the incrementing period, F is the cumulative water-gas ratio, and K is the maximum cumulative water-gas ratio after the gas well is shut in after being flooded.

[0061] Preferably, when the growth rate reaches the initial stage of growth, the risk of water flooding and well shut-in is low, which is the first stage of drainage and gas production, and no measures are required; when the growth rate reaches the middle stage of growth, the risk of water flooding and well shut-in is moderate, which is the second stage of drainage and gas production, and necessary drainage and gas production measures are taken according to the situation; when the growth rate reaches the late stage of growth, the risk of water flooding and well shut-in is very high, which is the third stage of drainage and gas production, and drainage and gas production measures must be taken.

[0062] Preferably, the initial increment is m(1T) < 0.63, the intermediate increment is 0.63 ≤ m(2T) ≤ 0.86, and the late increment is 0.86 < m(3T) ≤ 0.95.

[0063] The initial stage of the increase is within the first period T; the middle stage of the increase is within the second period 2T; and the late stage of the increase is within the third period 3T.

[0064] This invention provides a simple and rapid method for predicting the liquid accumulation trend and determining the timing of drainage and gas production in tight gas reservoirs based on gas well production data. It is applicable to gas fields with a large number of producing wells and fluctuating production data, providing a quantitative method for selecting the timing of drainage and gas production. This invention is based on the fundamental understanding obtained from relative permeability experiments in tight, low-permeability carbonate gas reservoirs: different water production characteristics of gas wells are controlled by different pore structures and water activity in the reservoir. Based on this understanding, a mathematical model for selecting the timing of drainage and gas production can be established by analyzing the variation patterns of gas well production data. This invention does not require gas well oil and casing pressure data, only daily water and gas production data, reducing the requirements for gas well production processes, possessing universal applicability, and providing a classification of "low, medium, and high" urgent timing for drainage and gas production, reducing the lag in drainage and gas production measures and helping to improve the implementation effect of drainage and gas production.

[0065] The specific implementation process of this invention is as follows:

[0066] 1. Based on the daily water production and daily gas production at the wellhead, calculate the cumulative water production W, the cumulative gas production of the gas well, and the cumulative water-gas ratio F (cumulative water production / cumulative gas production). Use the cumulative production data to reduce the interference of the daily production data jumps on the prediction, and plot the curve of the cumulative water-gas ratio as a function of the number of production days.

[0067] II. Based on the cumulative water-gas ratio change curve, determine the type of water-gas ratio change in the gas well: stable, decreasing, increasing, or a combination of both. A combination type is a stable water-gas ratio in the initial stage plus an increasing ratio in the later stages. The stable type does not consider drainage and gas production measures, but the increasing type requires such measures. This invention addresses the case where the cumulative water-gas ratio of the gas well is increasing.

[0068] During the continuous extraction process of gas wells, the water phase flow capacity in the reservoir increases with the increase of the production pressure difference, which reduces the gas phase flow capacity in the gas-water two-phase flow. As a result, the production water-gas ratio (cumulative water production / cumulative gas production) will mainly increase throughout the entire life cycle of the gas well.

[0069] Third, when the cumulative water-gas ratio curve of a gas well shows an increasing phenomenon, a corresponding increasing mathematical model should be established. Different geological conditions and production systems of gas wells make it difficult to classify their actual life cycle solely by increasing, decreasing, or stable patterns; they often exhibit a certain combination. However, the complete life cycle will be characterized primarily by increasing trends, with varying rates of increase, showing exponential distribution characteristics. The control parameters K and T of the exponential function should be solved using the least squares method. When solving complex exponential functions using the least squares method, the function needs to be linearized, transforming the differential equation into a corresponding difference equation, and then into a linearized equation. The model parameters are then solved using the least squares method.

[0070] Because the daily water-gas ratio data for a single well is affected by the actual switching regime, it suffers from problems such as being scattered, disorganized, and complex. Figure 1 As shown, the cumulative water-to-gas ratio F(t) (cumulative water production / cumulative gas production), where each time t corresponds to one F, results in the curve shown in the attached figure. Figure 1 The broken line represents the cumulative change in the daily water-to-air ratio, reducing the daily water-to-air ratio data (see attached diagram). Figure 1 The central ▲ point represents the fluctuation of the daily water-to-gas ratio (daily water production / daily gas production) at each moment, which has an intuitive regularity.

[0071] like Figure 2 As shown, the actual water-gas ratio is a scatter plot, which is a known value (each time period corresponds to an F, F = cumulative water production / cumulative gas production). The actual cumulative water-gas ratio data needs to be expressed by a mathematical function to represent its changing pattern. That is, formula (1) is chosen to describe the exponential change pattern of this data. K and T are solved according to mathematical methods, that is, the mathematical model of the well is determined:

[0072]

[0073] In this invention, parameter T represents the increasing period of the cumulative water-gas ratio. The smaller the value of T, the greater the rate of increase in the water-gas ratio of the producing well, the higher the risk of flooding, and the shorter the lifespan of the gas well. The maximum cumulative water-gas ratio of the gas well during its natural production cycle is also the maximum cumulative water-gas ratio after the gas well is shut down due to flooding.

[0074] The method for solving for control parameters K and T using the least squares method is as follows:

[0075] By solving for the control parameters K and T in equation (1), the cumulative water-to-gas ratio exponential function is finally determined. When using the least squares method to solve complex exponential functions, the function needs to be linearized.

[0076] First, solve the differential equation of function (1) (equation (2)). Since the cumulative water-air ratio data belongs to the data with equal time intervals, the above differential equation can be transformed into the corresponding difference equation, and then into a linearized equation. Then, the model parameters are solved by the least squares method.

[0077] The differential equation TF'+F=K is given by equation (2).

[0078] F' is the derivative of F. By differentiating formula (1) and simplifying, we can obtain formula (2).

[0079] Convert it into a difference equation (a method for numerically solving derivatives).

[0080] Where the time interval is a constant, i.e., Δt = t i+1 -t i = constant, F i For the corresponding t i The cumulative water-to-air ratio over a period of time, F i+1 Corresponding to t i+1 The cumulative water-to-air ratio over a given time period.

[0081]

[0082] Simplifying the difference equation, we get:

[0083]

[0084] Equation (4) is a linear equation. Therefore, the optimal parameters T and K can be obtained by using the least squares method, thereby determining the water-gas ratio increasing model of the water-gas well.

[0085] IV. Establish a prediction function for the probability of water flooding in gas wells, i.e., classify different urgent situations for implementing drainage and gas production measures. For example... Figure 3 As shown, when the rate of increase reaches the initial stage (within the first cycle T), the risk of water flooding and shutting down the gas well is low, which is the first stage of drainage and gas production and is not serious; when the rate of increase reaches the middle stage (within the second cycle 2T), the risk of water flooding and shutting down the well is moderate, which is the second stage of drainage and gas production and certain drainage and gas production measures should be taken; when the rate of increase reaches the late stage (within the third cycle 3T), the risk of water flooding and shutting down the well is very high, which is the third stage of drainage and gas production and effective drainage and gas production measures must be implemented immediately.

[0086]

[0087]

[0088]

[0089]

[0090] In this invention, when determining the timing of drainage and gas production, the cumulative water-to-gas ratio data of the gas well at different periods is first obtained. Then, according to mathematical methods, the T and K of the water-to-gas ratio index model are fitted to determine the m in different time periods, i.e., the probability of flooding (the current cumulative water-to-gas ratio is the ratio of the final flooding). Then, according to the three stages of the flooding probability (0-0.63 is the early stage), (0.63-0.85 is the middle stage), and (0.85-0.96 is the late stage), the gas well is currently in which interval, and thus the urgent timing of drainage and gas production measures is determined.

[0091] This invention solves the problems of blindness, complexity, and lag in drainage gas production. It establishes a more adaptable and standardized method for selecting the timing of drainage gas production, which can promptly grasp the water flooding trend of gas wells, plan drainage gas production measures in advance, and scientifically take corresponding drainage gas production measures in the early, middle, and late stages of the water-to-gas ratio increase, thereby improving the efficiency of drainage gas production.

[0092] Based on the actual cumulative water-gas ratio curve and its variation pattern of the well to be judged, the fitted water-gas ratio exponential equation is as follows: (K = 2.29, the cumulative water-gas ratio of the final gas well without drainage and gas production measures; T = 150, an exponentially increasing cycle every 150 days). For example... Figure 4 As shown, when t = 400 days, between 2T(300) < 400 < 3T(450), it is the third cycle of drainage and gas production, and drainage and gas production measures need to be carried out urgently. At this time, according to the production status of the gas well, the drainage and gas production measures of plunger gas lift are implemented on site, which significantly reduces the increasing trend of cumulative water-gas ratio, indicating that the drainage and gas production implementation effect is significant.

[0093] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention. Many other changes and modifications can be made without departing from the concept and scope of the present invention. It should be understood that the appended claims define the scope of the present invention, which is not limited to the specific embodiments. Components, structures, and method steps not described in detail in this embodiment are all well-known components, common structures, or common means in the industry, and will not be described in detail here.

Claims

1. A quantitative method for determining the timing of drainage and gas production in low-permeability gas wells, characterized in that: The specific steps are as follows: Step 1: Based on the daily water production at the gas wellhead q w and daily gas production q g Calculate the cumulative water production W and cumulative gas production G of the gas well within the required number of days; Step two: Based on the cumulative water production W and cumulative gas production G obtained in Step one, obtain the cumulative water-gas ratio F, and plot the curve of the cumulative water-gas ratio changing with the number of production days; when the curve shows an increasing phenomenon, establish a corresponding increasing mathematical model; the increasing model of the cumulative water-gas ratio F in the increasing period is an exponential function: ， In the formula, T is the increment period; K is the maximum cumulative water-gas ratio after the gas well is shut in with water; t is the time, in days. Step 3: Based on the established incremental mathematical model, establish a prediction function for the probability of water flooding in gas wells, and determine the different urgency levels for implementing drainage and gas production measures; the prediction function for the probability of water flooding in gas wells is: ， In the formula, T is the incrementing period, F is the cumulative water-gas ratio, K is the maximum cumulative water-gas ratio after the gas well is shut down by water flooding, i is the i-th, and F(iT) is the cumulative water-gas ratio under the i-th incrementing period. When determining the timing of drainage and gas production, the cumulative water-to-gas ratio data of the gas well at different times is first obtained. Then, according to mathematical methods, the T and K of the water-to-gas ratio index model are fitted to determine the m in different time periods, i.e., the probability of flooding. Then, according to the three stages of flooding probability, the gas well is currently in which interval, and thus the urgent timing of drainage and gas production measures is determined.

2. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 1, characterized in that: In step one, Cumulative gas production: , Cumulative water production: , In the above formula, t represents the number of days.

3. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 1, characterized in that: In step two, the cumulative water-to-gas ratio F is the cumulative water production / cumulative gas production. Cumulative water-air ratio: In the formula, t represents the number of days.

4. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 1, characterized in that: In step two, the control parameters T and K are obtained using the least squares method, thereby determining the water-gas ratio increasing model for the water-producing gas well.

5. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 4, characterized in that: When using the least squares method to find the control parameters of the exponential function, the exponential function is first linearized, and the differential equation of the exponential function is solved. Then, the differential equation is transformed into the corresponding difference equation, and then into a linearized equation. Finally, the control parameters T and K of the increasing model are solved by the least squares method.

6. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 1, characterized in that: When the growth rate reaches the initial stage, the risk of water flooding and shutting down the gas well is low, which is the first stage of drainage and gas production, and no measures are required. When the growth rate reaches the middle stage, the risk of water flooding and shutting down the well is moderate, which is the second stage of drainage and gas production, and necessary drainage and gas production measures are taken according to the situation. When the growth rate reaches the late stage, the risk of water flooding and shutting down the well is very high, which is the third stage of drainage and gas production, and drainage and gas production measures must be taken.

7. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 6, characterized in that: The initial stage of the increase is m(1T) < 0.63, the middle stage of the increase is 0.63 ≤ m(2T) ≤ 0.86, and the late stage of the increase is 0.86 < m(3T) ≤ 0.

95.

8. The quantitative judgment method for determining the timing of drainage and gas production in low-permeability gas wells according to claim 7, characterized in that: The initial stage of the increase is within the first period T; the middle stage of the increase is within the second period 2T; and the late stage of the increase is within the third period 3T.

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