A method for predicting stage recovery of natural decline gas well

Abstract

This invention relates to the field of oil and gas field development technology, specifically to a method for predicting the stage recovery degree of naturally declining gas wells. The method includes the following steps: Step 1: Calculate the end time of stable production; Step 2: Determine the relationship between the end time and the end time of stable production; When the end time < the end time of stable production, proceed to Step 3; When the end time ≥ the end time of stable production, proceed to Step 4; Step 3: Calculate the stage recovery degree of the stable production stage; Step 4: Calculate the stage recovery degree of the declining stage. This invention establishes a full-stage production capacity equation for constant-volume gas-driven reservoirs and proposes an approximate solution for the pressure conversion skin, which can be used to calculate the average formation pressure of constant-volume gas-driven reservoirs throughout all stages, providing important theoretical support for the full-stage dynamic analysis of constant-volume gas-driven reservoirs.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, and specifically to a method for predicting the stage recovery level of naturally declining gas wells. Background Technology

[0002] A common practical problem encountered in gas well production is: given the relevant parameters of a gas well at a certain moment, what will be the cumulative gas production at a future point in time? Cumulative gas production at a given stage represents the absolute gas production capacity of a gas well at a particular stage. However, since different gas wells have different controlled reserves, comparisons between different wells are not convenient. Stage recovery rate, on the other hand, represents the relative gas production capacity of a gas well at a particular stage and can be used to compare the stage production capacity of gas wells. Therefore, this practical problem can be extended to: given the relevant parameters of a gas well at a certain moment, what will be the stage recovery rate at a future point in time?

[0003] The production process of naturally declining gas wells can be divided into two stages: stable production and decline. The calculation methods for the recovery degree differ depending on the stage the well is in. To address this practical problem, production capacity equations for both the stable and decline stages are needed. However, existing production capacity equations are limited to the stable production stage and lack equations for the decline stage, making it difficult to accurately obtain the recovery degree during this phase. Establishing a method for predicting the recovery degree of naturally declining gas wells, enabling simultaneous prediction of both the stable and decline stages, is of significant value for gas well production and gas field development. Summary of the Invention

[0004] The present invention aims to address the above-mentioned problems by proposing a method for predicting the stage recovery rate of naturally declining gas wells.

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

[0006] For a constant-volume gas-driven well, its full-stage production capacity equation can be expressed as:

[0007]

[0008] In the formula: q sc (t) represents the wellhead gas production at time t, in m 3 / d;

[0009] The pseudo-mean formation pressure at time t, in MPa 2 / mPa·s;

[0010] Let be the average formation pressure at time t, in MPa;

[0011] ψ(p wf (t) represents the pseudo-bottomhole flowing pressure at time t, in MPa.2 / mPa·s;

[0012] p wf (t) is the bottom hole flowing pressure at t, MPa;

[0013] p sc is the standard pressure, MPa;

[0014] Z sc is the standard deviation coefficient, dimensionless;

[0015] T sc is the standard temperature, K;

[0016] T is the reservoir temperature, K;

[0017] K is the reservoir permeability, 10 -3 μm 2 ;

[0018] h is the reservoir thickness, m;

[0019] S p (i) is the initial value of the pressure conversion skin, dimensionless;

[0020] μ i is the corresponding gas viscosity, mPa·s; i is the corresponding gas viscosity, mPa·s;

[0021] μ wf (t) is the corresponding gas viscosity, mPa·s; wf (t) is the corresponding gas viscosity, mPa·s;

[0022] t D is the dimensionless production time, t D = t / 1, t D > 0, dimensionless;

[0023] wherein the relationship between the pseudo-pressure ψ(p) and the pressure p is:

[0024]

[0025] The relationship between the pressure p and the pseudo-pressure ψ(p) can be obtained by transforming equation (2):

[0026]

[0027] In the formula: ψ(p) is the pseudo-pressure corresponding to the pressure p, MPa 2 / mPa·s;

[0028] p is the pressure, MPa;

[0029] p0 is the reference pressure, MPa;

[0030] a is μ(p)Z(p)-p 2 The curve is obtained by linear fitting, and the first coefficient is dimensionless.

[0031] b is μ(p)Z(p)-p 2 The curve uses the second coefficient obtained through linear fitting, which is dimensionless.

[0032] μ(p) is the gas viscosity corresponding to pressure p, in mPa·s;

[0033] Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless;

[0034] The initial value of the pressure conversion skin is S. p (i):

[0035]

[0036] In the formula: ψ(p) i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s;

[0037] p i The original formation pressure is expressed in MPa.

[0038] ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0039] p wf (1) is the bottom hole pressure at t=1, in MPa;

[0040] q sc (1) is the wellhead gas production at t=1, m 3 / d;

[0041] For a constant-volume gas-driven well, the mass balance equation is:

[0042]

[0043] In the formula: Z r (t) is The corresponding deviation coefficient is dimensionless.

[0044] Z i For p i The corresponding deviation coefficient is dimensionless.

[0045] G represents the controlled reserves of the gas well, m 3 ;

[0046] G p (t) represents the cumulative gas production at time t, m 3 ;

[0047] A common practical problem encountered during gas well production is: when a gas well starts producing gas from a certain time t... B Start, production until time t E End, from t B to t E During this period, the cumulative gas production at each stage is unknown. The cumulative gas production at a stage represents the absolute gas production capacity of a gas well at a certain stage. However, since different gas wells have different controlled reserves, comparisons between different gas wells are not convenient. The stage production level represents the relative gas production capacity of a gas well at a certain stage and can be used to compare the stage production capacity of gas wells. Therefore, this practical problem can be extended to: when a gas well... B Start, production until time t E End, from t B to t E During this period, the corresponding stage extraction degree η(Δt) is unknown.

[0048] Gas well production can be divided into two stages: a stable production stage and a declining production stage. The gas well's production rate is q. sc * To achieve stable production, the bottom hole flowing pressure p wf (t) continuously decreases, when p wf (t) Reduce to the minimum bottom pressure of the export well p wf * At this point, the gas well enters a declining phase. Therefore, it is necessary to predict the gas well in two phases: the stable production phase and the declining phase.

[0049] (1) Stable production stage

[0050] When a gas well is in a stable production phase, p wf (t) typically decreases linearly with t, therefore a stable production end time t can be established. * Predictive formula:

[0051]

[0052] In the formula: t * The end time for stabilizing production, d;

[0053] int(x) is the floor function. If x = 1.1, then int(x) = 1; if x = 1.9, then int(x) = 1. Since the unit of x is d, the unit of int(x) is also d.

[0054] t B Given the start time, t is required. B ≥2, d;

[0055] p wf (t B ) for t BThe well bottom flowing pressure at the time, MPa;

[0056] p wf * The well bottom flowing pressure at the time, p wf * = constant, MPa;

[0057] The well bottom flowing pressure at the time, p wf The slope of the linear fitting of the (t)-t curve, dimensionless;

[0058] When the ending time t E <The stable production ending time t * , the gas well is in the stable production stage, and the stage cumulative gas G p (Δt) S at the time is:

[0059] G p (Δt) S = q sc * (t E -t B ) (7)

[0060] In the formula: G p (Δt) S is the stage cumulative gas in the stable production stage, m 3 .

[0061] t E is the ending time, t E >t B , d;

[0062] According to the definition of the recovery degree, the calculation formula of the stage recovery degree η(Δt) S in the stable production stage is:

[0063]

[0064] In the formula: η(Δt) S is the stage recovery degree in the stable production stage, dimensionless;

[0065] q sc * is the wellhead gas production in the stable production stage, q sc * = constant, m 3 / d;

[0066] (2) Decline stage

[0067] When the ending time t E ≥ stable production ending time t * , the gas well is in the decline stage, and the stage cumulative gas Gp (Δt) D The formula for calculation is:

[0068]

[0069] In the formula: G p (Δt) D For the cumulative gas production during the decreasing phase, m 3 .

[0070] Represents q sc The summation of (t), where t takes values ​​from t * +1 to t E m 3 / d;

[0071] The level of extraction during the decreasing phase, η(Δt). D The formula for calculation is:

[0072]

[0073] In the formula: η(Δt) D The level of extraction during the decreasing phase is dimensionless.

[0074] In equations (9) and (10), due to the decreasing phase q sc The expression for (t) is unknown and requires further derivation.

[0075] When a gas well is in the decline phase, due to the decline phase p wf (t)=p wf * Equation (1) can be transformed into:

[0076]

[0077] In the formula: ψ(p) wf * ) is p wf * Corresponding simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0078] Equation (5) can be transformed into:

[0079]

[0080] In the formula: G p (t-1) represents the cumulative gas production at time t-1, m 3 ;

[0081] in, With Z r The following transformation relationship exists between (t):

[0082]

[0083] In the formula: A is The curve is obtained by linear fitting, and the first coefficient is dimensionless.

[0084] B is The curve uses the second coefficient obtained through linear fitting, which is dimensionless.

[0085] There are two unknown parameters in equations (11) and (12). and q sc (t), which can be solved iteratively:

[0086] (1) During iterative calculation, let q in equation (12) sc (t) = initial value q during iteration sc (t) B Then equation (12) becomes:

[0087]

[0088] In the formula: q sc (t) B m is the initial value for the gas production during the decreasing phase of the iteration. 3 / d, q sc (t) B The range of values ​​is [1, q]. sc * ];

[0089] (2) During iterative calculation, let q in equation (11) sc (t) = Iteration final value q sc (t) E Then equation (11) becomes:

[0090]

[0091] In the formula: q sc (t) E m is the final value of the gas production during the decreasing phase of the iteration. 3 / d;

[0092] (3) During iterative calculation, the solution is achieved by setting an iteration stopping condition. The iteration stopping condition is:

[0093] |q sc (t) B -q sc (t) E | / q sc (t) E ≤ε(q sc (16)

[0094] In the formula: |q sc (t) B -q sc (t) E | / q sc (t) E The iteration error is dimensionless.

[0095] ε(q sc ) represents the upper limit of the iteration error, 0 ≤ ε(q) sc ≤10%, dimensionless;

[0096] Since it is the decreasing phase, the calculation time t takes the value from t * +1 to t E Therefore, it is necessary to iterate over different t values ​​one by one. The steps of the time-by-time iteration are as follows:

[0097] (1) Let t = t * +1, at this point G p (t-1)=G p (t * )=q sc * t * By iteratively solving equations (11) and (12), we obtain q at this point. sc (t), output q sc (t * +1)=q sc (t);

[0098] (2) Let t = t * +2, at this point G p (t-1)=G p (t * +1)=q sc * t * +q sc (t * +1), and by iteratively solving equations (11) and (12), we obtain q at this point. sc (t), output q sc (t * +2)=q sc (t);

[0099] Iterate by increasing the value of t one by one until t = t E When the iteration ends, t * +1 to t E q at time sc Substituting (t) into equation (10), the stage extraction degree is calculated.

[0100] The technical effects of this invention are as follows:

[0101] This invention establishes the full-stage productivity equation for constant-volume gas-driven gas reservoirs and proposes an approximate solution for the pressure transition skin, which can be used to calculate the average formation pressure of constant-volume gas-driven gas reservoirs throughout the entire process, providing important theoretical support for the full-stage dynamic analysis of constant-volume gas-driven gas reservoirs. Attached Figure Description

[0102] Figure 1 This is a diagram showing gas production and bottom hole flowing pressure.

[0103] Figure 2 The diagram shows the process and results of the first time-by-time iteration.

[0104] Figure 3 The diagram shows the process and results of the second time-by-time iteration.

[0105] Figure 4 The diagram shows the process and results of the third time-by-time iteration.

[0106] Figure 5 The figures show the calculation results and numerical simulation results of this invention. Detailed Implementation

[0107] A method for predicting the stage recovery rate of naturally declining gas wells, the method is as follows:

[0108] Step 1: Calculate the end time t of stable production using formula (6). * ;

[0109] Step 2: Determine the end time t E With the end time of stable production t * Relationship;

[0110] When the end time t E <End time of stable production t * Then, proceed to step 3;

[0111] When the end time t E ≥ Production stabilization end time t * Then, proceed to step 4;

[0112] Step 3: Calculate the stage extraction degree η(Δt) of the stable production stage using formula (8). S ;

[0113] Step 4: Calculate the stage recovery rate η(Δt) during the decline phase. D ;

[0114] Step 4.1: Let p take the value p wf * p i p wf (1) The pseudo-original formation pressure ψ(p) is calculated using formula (2). i), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1)), p wf * Simulated bottom hole flowing pressure ψ(p) wf * );

[0115] Step 4.2: Calculate the initial value S of the pressure conversion skin using formula (4). p (i);

[0116] Step 4.3: Determine the start time t of the decline phase * +1, let t = t * +1, at this point G p (t-1)=q sc * t * ;

[0117] Step 4.4: Iteratively calculate the gas production q during the decreasing phase on an hourly basis. sc (t)

[0118] (1) Perform iteration at time t

[0119] ① Assume the initial value of the iteration is q sc (t) B q sc (t) B The range of values ​​is [1, q]. sc * ];

[0120] ② Calculated using formula (14)

[0121] ③ Calculate the mean formation pressure using formula (13)

[0122] ④ Let p take a value The pseudo-average formation pressure is calculated using formula (2).

[0123] ⑤ Calculate the final value q of the iteration using formula (15) sc (t) E ;

[0124] ⑥ Determine the initial value q for the gas production during the decreasing phase. sc (t) B The iterative final value q of the gas production during the decreasing phase sc (t) E Does the iteration error between them satisfy formula (16)?

[0125] If not satisfied, let q sc (t)B =q sc (t) E Repeat steps ② through ⑥ to continue iterating;

[0126] If satisfied, let q sc (t)=q sc (t) E Output q at this time. sc (t), proceed to step (2) and perform time-by-time iteration;

[0127] (2) Time-by-time iteration

[0128] When t < end time t E When t is incremented by 1, the new t is used, and the current G is incremented by 1. p (t-1) Increase q sc (t) is then used as the new G p (t-1), repeat step 4.4 iteratively until t = end time t. E ;

[0129] When t = end time t E When the time-by-time iteration ends, execute (3);

[0130] (3) Calculate the stage recovery rate η(Δt) during the decline phase. D

[0131] The stage extraction degree η(Δt) during the decreasing phase can be calculated using the following formula (10). D .

[0132] Specific experimental examples

[0133] Gas well C is a numerical simulation gas well. The gas production and bottom hole flowing pressure of well C are shown in [reference needed]. Figure 1 It can be seen that well C starts to decrease from 452 d. The starting time t is chosen as... B The time limit is 99 days, and its basic parameters are shown in Table 1. To fully verify the reliability of the present invention, the end time t was selected. E The iteration error upper limit ε(q) is given by values ​​of 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1000 d respectively. sc The value was set to 0.01%, and the calculation and verification were performed using this invention. The specific calculation process is as follows.

[0134] Table 1 Basic Parameters Table

[0135]

[0136] A method for predicting the stage recovery rate of naturally declining gas wells, the method is as follows:

[0137] Step 1: Calculate the end time t of stable production using formula (6). * =464 d;

[0138] Step 2: Determine the end time t E With the end time of stable production t * Relationship;

[0139] Due to the end time t E Values ​​d and t are taken as 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000. * =464d, therefore:

[0140] (1) When t E When the value is 100, 200, 300, or 400, t satisfies E <t * Proceed to step 3;

[0141] (2) When t E When the value is 500, 600, 700, 800, 900, 1000, the condition t is satisfied. E ≥t * Proceed to step 4;

[0142] Step 3: Calculate the stage extraction level during the stable production phase;

[0143] The stage extraction level during the stable production phase is calculated using formula (8); specifically:

[0144] When t E When η = 100, η(Δt) S =0.05%;

[0145] When t E When η = 200, η(Δt) S =4.66%;

[0146] When t E When η = 300, η(Δt) S =9.28%;

[0147] When t E When η = 400, η(Δt) S =13.90%;

[0148] Step 4: Calculate the stage extraction level during the decline phase;

[0149] Step 4.1: Let p take the value p wf * p i p wf (1), calculated using formula (2)

[0150] ψ(p wf * ) = 1824.26 MPa 2 / mPa·s;

[0151] ψ(p i = 46220.42MPa 2 / mPa·s;

[0152] ψ(p wf (1))=24307.48MPa 2 / mPa·s;

[0153] Step 4.2: Calculate the initial value S of the pressure conversion skin. p (i);

[0154] The initial value S of the pressure conversion skin is calculated using formula (4). p (i) = 6.67;

[0155] Step 4.3: Determine the start time t of the decline phase * +1

[0156] Let t = t * +1 = 465d, at this point G p (t-1)=q sc * t * =32480000m 3 ;

[0157] Step 4.4: Calculate q in the decreasing phase iteratively time by time. sc (t);

[0158] (1) Perform iteration at time t

[0159] During the first iteration:

[0160] ① Assume the initial value of the iteration is q sc (t) B =70000m 3 / d, satisfying q sc (t) B The value range is between [1, q] sc * ], where q can be found in Table 1 sc * =70000m 3 / d;

[0161] ②Calculate using formula (14)

[0162] ③The mean formation pressure is calculated using formula (13).

[0163] ④ Let p take a value The result is obtained by formula (2).

[0164] ⑤ The final value q of the iteration is calculated using formula (15). sc (t) E =68617.46m 3 / d;

[0165] ⑥ Calculate q sc (t) B With q sc (t) E The iteration error between them is 2.01%, which does not satisfy formula (16);

[0166] Let q sc (t) B =q sc (t) E Repeat steps ② through ⑥ for the second iteration;

[0167] During the second iteration:

[0168] ②Calculate using formula (14)

[0169] ③The mean formation pressure is calculated using formula (13).

[0170] ④ Let p take a value The result is obtained by formula (2).

[0171] ⑤ The final value q of the iteration is calculated using formula (15). sc (t) E =68619.03m 3 / d;

[0172] ⑥ Calculate q sc (t) B With q sc (t) E The iteration error between them is 0.002%, which satisfies formula (16);

[0173] Let q sc (t)=q sc (t) E Proceed to step (2) and perform time-by-time iteration;

[0174] (2) Time-by-time iteration

[0175] Because of t EGiven values ​​of 500, 600, 700, 800, 900, and 1000, and a current t = 465d, the condition t < t0 is satisfied. E Increment the current t by 1 and use it as the new t, while simultaneously setting the current G... p (t-1) Increase q sc (t) is then used as the new G p (t-1), repeat step 4.4 iteratively until t. E =t, the time-by-time iteration ends, execute (3);

[0176] To facilitate the demonstration of the calculation process, the initial value for each hourly iteration is assumed to be q. sc (t) B =70000m 3 / d, the process and results of time-by-time iteration are shown in [link / d]. Figures 2 to 4 ;

[0177] Figure 2 This is the process and result of the first time-by-time iteration. The results show that q at different times... sc (t) B With q sc (t) E None of them satisfy formula (16), let q sc (t) B =q sc (t) E Then proceed with the second iteration;

[0178] Figure 3 This section presents the process and results of the second time-by-time iteration. The results show that when the value of t is between 465 and 518d, q sc (t) B With q sc (t) E The iteration error between them satisfies formula (16), let q sc (t)=q sc (t) E When t takes values ​​between 519 and 1000d, q sc (t) B With q sc (t) E The iteration error between them does not satisfy formula (16), let q sc (t) B =q sc (t) E Then proceed to the third iteration;

[0179] Figure 3 The process and results of the third time-by-time iteration are shown. The results indicate that when the value of t is between 519 and 1000d, after the third time-by-time iteration, q sc (t)B With q sc (t) E The iteration error between them satisfies formula (16), let q sc (t)=q sc (t) E .

[0180] Because of t E The values ​​are 500, 600, 700, 800, 900, and 1000. Therefore, when the corresponding time is calculated, (3) is executed.

[0181] (3) Calculate the stage recovery rate during the decline phase.

[0182] The stage extraction degree during the decline is calculated using formula (10):

[0183] When t E When η = 500, η(Δt) D =18.45%;

[0184] When t E When η = 600, η(Δt) D =22.55%;

[0185] When t E When η = 700, η(Δt) D =26.22%;

[0186] When t E When η = 800, η(Δt) D =29.53%;

[0187] When t E When η = 900, η(Δt) D =32.50%;

[0188] When t E When η = 1000, η(Δt) D =35.20%.

[0189] This invention calculates t E The stage extraction degree η(Δt) is calculated when the values ​​are 100, 200, 300, 400, 500, 600, 700, 800, 900, and 1000 days, respectively. S and η(Δt) D The calculation results of this invention are compared with the numerical simulation results, and the results are shown in the figure. Figure 5 As can be seen, the two are almost identical, with the absolute value of the relative error ranging from 0.00% to 0.49%, showing high precision and demonstrating the reliability of the invention.

Claims

1. A method for predicting the stage recovery rate of a naturally declining gas well, characterized in that: The method is as follows: Step 1: Calculate the end time t of stable production * ; By using the following formula (6) In the formula: t * The end time for stabilizing production, d; int(x) is the floor function. If x = 1.1, then int(x) = 1; if x = 1.9, then int(x) = 1. Since the unit of x is d, the unit of int(x) is also d. t B Let t be the start time. B ≥2, d; p wf (t B ) for t B Bottom hole flowing pressure at that time, MPa; p wf * For the bottom hole flowing pressure during the decreasing phase, p wf * = constant, MPa; α represents p during the stable production stage. wf The slope of the (t)-t curve is obtained by linear fitting and is dimensionless; The calculated end time t of stable production * ; Step 2: Determine the end time t E With the end time of stable production t * Relationship; When the end time t E <End time of stable production t * Then, proceed to step 3; When the end time t E ≥ Production stabilization end time t * Then, proceed to step 4; Step 3: Calculate the stage extraction degree η(Δt) during the stable production phase. S ; By using the following formula (8) In the formula: η(Δt) S The level of extraction during the stable production phase is dimensionless. q sc * q represents the wellhead gas production during the stable production phase. sc * = constant, m 3 / d; G represents the controlled reserves of the gas well, m 3 ; t E Given the end time, t is required. E >t B ,d; The stage extraction degree η(Δt) during the stable production phase is calculated. S ; Step 4: Calculate the stage recovery rate η(Δt) during the decline phase. D ; Step 4.1: Let p take the value p wf * p i p wf (1) By using the following formula (2) In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s; p represents pressure, in MPa; p0 is the reference pressure, in MPa; a is μ(p)Z(p)-p 2 The curve is obtained by linear fitting, and the first coefficient is dimensionless. b is μ(p)Z(p)-p 2 The curve uses the second coefficient obtained through linear fitting, which is dimensionless. μ(p) is the gas viscosity corresponding to pressure p, in mPa·s; Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless; The pseudo-original formation pressure ψ(p) was calculated. i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1)), p wf * Simulated bottom hole flowing pressure ψ(p) wf * ); Step 4.2: Calculate the initial value S of the pressure conversion skin. p (i) By using the following formula (4) In the formula: S p (i) represents the initial value of the pressure conversion skin, which is dimensionless; Z sc The standard deviation coefficient is dimensionless. T sc Standard temperature, K; p sc Standard pressure, MPa; K is the reservoir permeability, 10 -3 μm 2 ; h is the reservoir thickness, in meters; T is the reservoir temperature, in K; ψ(p i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s; p i The original formation pressure is expressed in MPa. ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s; p wf (1) is the bottom hole pressure at t=1, in MPa; q sc (1) is the wellhead gas production at t=1, m 3 / d; The initial value S of the pressure conversion skin was calculated. p (i); Step 4.3: Determine the start time t of the decline phase * +1 Because of t * To determine the end time of stable production, t is defined as... * +1 represents the start time of the decreasing phase; let t = t * +1, at this point G p (t-1)=q sc * t * ; Step 4.4: Iteratively calculate the gas production q during the decreasing phase on an hourly basis. sc (t) (1) Perform iteration at time t ① Assume the initial value of the iteration is q sc (t) B q sc (t) B The range of values ​​is [1, q]. sc * ]; ② By using the following formula (14) In the formula: Let be the average formation pressure at time t, in MPa; Z r (t) is The corresponding deviation coefficient is dimensionless. Z i For p i The corresponding deviation coefficient is dimensionless. G p (t-1) represents the cumulative gas production at time t-1, m 3 ; q sc (t) B m is the initial value for the gas production during the decreasing phase of the iteration. 3 / d; Calculated ③ Calculate the mean formation pressure By using the following formula (13) In the formula: A is The curve is obtained by linear fitting, and the first coefficient is dimensionless. B is The curve uses the second coefficient obtained through linear fitting, which is dimensionless. The mean formation pressure was calculated. ④ Calculate the pseudo-mean formation pressure Let p take a value The pseudo-average formation pressure is calculated using formula (2). ⑤ Calculate the final value q of the iteration sc (t) E By using the following formula (15) In the formula: q sc (t) E m is the final value of the gas production during the decreasing phase of the iteration. 3 / d; ψ(p wf * ) is p wf * Corresponding simulated bottom hole flowing pressure, MPa 2 / mPa·s; The final value q of the iteration is calculated. sc (t) E ; ⑥ Determine the iteration error The initial value q for determining the gas production during the decreasing phase. sc (t) B The iterative final value q of the gas production during the decreasing phase sc (t) E Does the iteration error between them satisfy formula (16)? |q sc (t) B -q sc (t) E | / q sc (t) E ≤ε(q sc ) (16) In the formula: |q sc (t) B -q sc (t) E | / q sc (t) E The iteration error is dimensionless. ε(q sc ) represents the upper limit of the iteration error, 0 ≤ ε(q) sc ≤10%, dimensionless; If not satisfied, let q sc (t) B =q sc (t) E Repeat steps ② through ⑥ to continue iterating; If satisfied, let q sc (t)=q sc (t) E Output q at this time. sc (t), proceed to step (2) and perform time-by-time iteration; (2) Time-by-time iteration When t < end time t E When t is incremented by 1, the new t is used, and the current G is incremented by 1. p (t-1) Increase q sc (t) is then used as the new G p (t-1), repeat step 4.4 iteratively until t = end time t. E ; When t = end time t E When the time-by-time iteration ends, execute (3); (3) Calculate the stage recovery rate η(Δt) during the decline phase. D By using the following formula (10) In the formula: η(Δt) D The level of extraction during the decreasing phase is dimensionless. Represents q sc The summation of (t), where t takes values ​​from t * +1 to t E m 3 / d; The stage extraction rate η(Δt) during the decline is calculated. D .

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