A method for predicting target gas production of a naturally declining gas well

Abstract

The present application relates to the technical field of oil and gas field development, in particular to a target gas production rate prediction method for a natural decline gas well, which calculates the pseudo-original formation pressure, p wf (1) pseudo-well bottom flow pressure, p wf * pseudo-well bottom flow pressure at time t; and further calculates the initial value of the pressure conversion skin; calculates the start time of the decline stage; judges the relationship between the target production time and the start time of the decline stage, judges which stage the target production time is located in; if it is located in the stable production stage, the target production rate is the gas production rate of the stable production stage; otherwise, the gas production rate is calculated according to the decline stage. The present application establishes a full-stage deliverability equation for a constant-volume gas drive gas reservoir, proposes an approximate solution of the pressure conversion skin, which can be used to calculate the full-stage average formation pressure of the constant-volume gas drive gas reservoir, and provides important theoretical support for the full-stage dynamic analysis of the constant-volume gas drive gas reservoir.

Description

Technical Field

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

[0002] Gas well production typically faces a practical need: what is the target gas production rate when the well reaches a certain target time? To analyze this problem, gas well production needs to be divided into different stages for study. The actual gas well production process can generally be divided into two main stages: stable production and declining production. When the gas well is in the stable production stage, as long as the target time is still within the declining period, the target gas production rate is still equal to the stable production rate. When the gas well is in the declining production stage, due to the uncontrollable nature of the declining production analysis, predicting the target gas production rate in the declining stage is somewhat difficult.

[0003] In actual gas well operations, the stable production phase is typically short, followed by a natural decline phase that persists for an extended period. Therefore, when predicting target gas production at a known target time, the decline phase cannot be ignored. Existing gas well decline analysis theories are prone to multiple solutions. To address this issue, a new method for predicting target gas production in naturally declining gas wells is established using a full-stage production capacity equation. This method simultaneously predicts target gas production during both the stable and decline phases, which has significant practical implications for 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 target gas production 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 is:

[0007]

[0008] In the formula: The pseudo-mean formation pressure at time t, in MPa 2 / mPa·s;

[0009] The average formation pressure at time t, in MPa;

[0010] ψ(p wf (t) represents the pseudo-bottomhole flowing pressure at time t, in MPa. 2 / mPa·s;

[0011] p wf (t) represents the bottom hole flowing pressure at time t, in MPa;

[0012] p sc Standard pressure, MPa;

[0013] Z sc The standard deviation coefficient is dimensionless.

[0014] T sc Standard temperature, K;

[0015] T is the reservoir temperature, in K;

[0016] K is the reservoir permeability, 10 -3 μm 2 ;

[0017] h is the reservoir thickness, in meters;

[0018] q sc (t) represents the wellhead gas production at time t, in m 3 / d;

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

[0020] t D For dimensionless production time, t D =t / 1,t D >0, dimensionless.

[0021] The relationship between the pseudo-pressure ψ(p) and the pressure p is as follows:

[0022]

[0023] Transforming equation (2), we can obtain the relationship between pressure p and pseudo-pressure ψ(p):

[0024]

[0025] In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s;

[0026] p represents pressure, in MPa;

[0027] a is μ(p)Z(p)-p 2 The curve is obtained by linear fitting, and the first coefficient is dimensionless.

[0028] b is μ(p)Z(p)-p 2 The curve uses the second coefficient obtained through linear fitting, which is dimensionless.

[0029] μ(p) is the gas viscosity corresponding to pressure p, in mPa·s;

[0030] Z(p) is the deviation coefficient corresponding to pressure p, which is dimensionless;

[0031] Among them, the initial value S of the pressure conversion skin p (i) is:

[0032]

[0033] In the formula: ψ(p) i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s;

[0034] p i The original formation pressure is expressed in MPa.

[0035] ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0036] p wf (1) is the bottom hole pressure at t=1, in MPa;

[0037] q sc (1) is the wellhead gas production at t=1, m 3 / d.

[0038] For a constant-volume gas-driven well, the mass balance equation is:

[0039]

[0040] In the formula: Z r (t) is The corresponding deviation coefficient is dimensionless.

[0041] Z i The original formation pressure p i The corresponding deviation coefficient is dimensionless.

[0042] G represents the controlled reserves of the gas well, m 3 ;

[0043] G p (t) represents the cumulative gas production at time t, m 3 .

[0044] During the gas well production process, based on known t 0 q at time sc (t 0 ) and other parameters, and when the gas well reaches the target production time t T At that time, the corresponding target gas production q sc (t T The production stage of a gas well can be divided into a stable production stage and a declining production stage, where the gas production q during the stable production stage is unknown. sc (t)=q sc* = constant, bottomhole flowing pressure p during the decreasing phase wf (t)=p wf * =Constant. Needs to be solved separately.

[0045] (1) When a gas well is in a stable production phase, the bottom hole flowing pressure p wf (t) continuously decreases, when t = t * At -1, the well remains in a stable production phase, but the bottom hole flowing pressure p wf (t * -1) is usually unknown, when t = t * When it enters the natural decline stage, the bottom hole flowing pressure p wf * Given that if we take p wf (t * -1)≈p wf * Substituting into the capacity equation, the stable production phase exists:

[0046]

[0047]

[0048] In the formula: t * d represents the start time of the decreasing phase.

[0049] q sc * For the gas production during the stable production phase, m 3 / d;

[0050] ψ(p wf * ) is p wf * Simulated bottom hole flowing pressure at the time, MPa 2 / mPa·s;

[0051] p wf * The bottom hole flowing pressure during the decreasing phase is expressed in MPa.

[0052] Equations (6) and (7) both contain two unknown parameters. And t, can be solved simultaneously, the solution method is: use equation (6) to construct the mass balance equation. The curve, using equation (7) to derive the production capacity equation The curves intersect at a point on the x-axis, which represents the start time t of the decline phase of the gas well. * .

[0053] If the target production time is t T <Descent phase start time t *Then the target production time t T The corresponding target gas production q sc (t T The gas production q during the stable production phase is equal to the gas production during the stable production phase. sc * ;

[0054] If the target production time is t T ≥ Decreasing phase start time t * This indicates the target production time t T If it is in the decreasing phase, further judgment is required.

[0055] (2) When t = the start time of the decreasing phase t * At this point, the gas well enters a declining phase; as t continuously increases, the gas production q decreases. sc (t) continuously decreases, when t = target production time t T At that time, q sc (t)=q sc (t T According to equations (5) and (1), the decreasing phase exists:

[0056]

[0057]

[0058] 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;

[0059] q sc (t) E m is the final value of the gas production during the decreasing phase of the iteration. 3 / d;

[0060] G p (t-1) represents the cumulative gas production at time t-1, m 3 .

[0061] Therefore, an iterative approach can be used to solve this problem, where the stopping condition for iteration is:

[0062] |q sc (t) B -q sc (t) E | / q sc (t) E ≤ε(q sc (10)

[0063] In the formula: |q sc (t) B -q sc (t)E | / q sc (t) E The iteration error is dimensionless.

[0064] ε(q sc ) represents the upper limit of error for iterative calculation, 0 ≤ ε(q) sc ≤10%, dimensionless.

[0065] Let t = the start time of the decreasing phase. * Assume the initial value of the iteration is q. sc (t) B Calculated using equation (8) Calculate using equation (11) Will Substituting into equation (9), we can calculate the final value q of the iteration. sc (t) E If equation (10) is not satisfied, let q sc (t) B =q sc (t) E Continue iterating;

[0066] If equation (10) is satisfied, determine whether the production time t = target production time t is satisfied. T :

[0067] (1) If the calculation stops, output q. sc (t)=q sc (t) E ;

[0068] (2) If not satisfied, increase t by 1 to get the new t, that is, let t = t + 1, and iterate through step (2) to calculate the gas production q at that moment. sc (t), until the gas production q at that moment. sc (t) satisfies the iteration error requirement and also satisfies the condition that production time t = target production time t. T Output q sc (t T )=q sc (t), calculation ends.

[0069] In equations (6) and (8), With Z r The following transformation relationship exists between (t):

[0070]

[0071] In the formula: A is The curve is obtained by linear fitting, and the first coefficient is dimensionless.

[0072] B is The curve uses the second coefficient obtained by linear fitting, which is dimensionless.

[0073] The technical effects of this invention are as follows:

[0074] 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

[0075] Figure 1 The values ​​represent the gas production and bottom hole flowing pressure of well m29-4.

[0076] Figure 2 The mean formation pressure is given by the mass balance equation.

[0077] Figure 3 is the mean formation pressure in the productivity equation.

[0078] Figure 4 This is a diagram illustrating the start time of the decreasing phase.

[0079] Figure 5 This is a schematic diagram of the iterative calculation process.

[0080] Figure 6 For the present invention in different t T A diagram showing the calculation results and accuracy at that time. Detailed Implementation

[0081] A method for predicting the target gas production of a naturally declining gas well is as follows:

[0082] Step 1: When p takes the value p i p wf (1) p wf * At that time, 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 pressure ψ(p) wf * Then, the initial value S of the pressure conversion skin is calculated using formula (4). p (i);

[0083] Step 2: Calculate the start time t of the decreasing phase * ;

[0084] (1) Set the range of t to [1, t] T ];

[0085] (2) The mean formation pressure is calculated using material balance calculations based on formulas (6) and (11). Drawing the mass balance equation curve;

[0086] (3) The mean formation pressure is calculated using the production capacity equation and formulas (7) and (3). Drawing the capacity equation curve;

[0087] (4) The mass balance equation Curve and capacity equation When the curves are plotted on a graph, the x-axis corresponding to the intersection of the two curves represents the start time t of the decline phase of the gas well. * ;

[0088] Step 3: Determine the target production time t T With the start time t of the decreasing phase * Relationship;

[0089] If the target production time is t T <Descent phase start time t * Then the target production time t at that moment T The corresponding target output q sc (t T = Gas production q during the stable production phase sc * The calculation is now complete.

[0090] Conversely, if the target production time t T ≥ Decreasing phase start time t * Target production time t T If the process is in the decreasing phase, then step 4 needs to be executed to calculate the gas production q in the decreasing phase. sc (t).

[0091] Step 4: Calculate the gas production q during the decline phase. sc (t);

[0092] (1) Let the production time t = the start time of the decreasing phase t * ;

[0093] (2) Calculate the gas production q at time t. sc (t);

[0094] ① Assume the initial value of gas production for iteration is q sc (t) B Initial value q during iteration sc (t) B The range of values ​​is [1, q]. sc *];

[0095] ② The corresponding formula is obtained by calculation using formula (8). The corresponding mean formation pressure is calculated using formula (11).

[0096] ③ Let p in formula (2) take the following values. The corresponding pseudo-average formation pressure is calculated using formula (2). ④ The simulated average formation pressure Substituting into formula (9), the iterative final value q of the gas production is obtained. sc (t) E ;

[0097] ⑤ Determine the initial value q for iteration sc (t) B With the final value q of the iteration sc (t) E Does the iteration error between them satisfy formula (10)? If it does, let q sc (t)=q sc (t) E ;Execute directly ⑥;

[0098] If not satisfied, let q sc (t) B =q sc (t) E Repeat steps ① to ⑤ to continue iterating until the iteration error satisfies formula (10), then output q. sc (t)=q sc (t) E ;Execute ⑥;

[0099] ⑥ Determine the target production time t T Relationship with production time t;

[0100] If production time t = target production time t T Output q sc (t T )=q sc (t), calculation ends;

[0101] If production time t < target production time t T Execute (3);

[0102] (3) Increment t by 1 to get the new t, that is, let t = t + 1, and iterate through step (2) to calculate the gas production q at this moment. sc (t), until the gas production q at that moment. sc (t) satisfies the iteration error requirement and also satisfies the condition that production time t = target production time t. T Output q sc (tT )=q sc (t), calculation ends.

[0103] Specific experimental examples

[0104] The invention was implemented and verified using a numerical simulation of well m29-4. The basic calculation parameters of well m29-4 are shown in Table 1, and the gas production and bottom hole flowing pressure are shown in... Figure 1 It can be seen that: well m29-4 has a depth of 60,000 m 3 The gas production rate was stabilized at / d, and the bottom hole pressure continued to decrease. When the production time was 457 days, the bottom hole pressure decreased to 10MPa, and the well entered the natural decline stage.

[0105] Table 1 Basic Parameters Table

[0106]

[0107] A method for predicting the target gas production of a naturally declining gas well is as follows:

[0108] Step 1: When p takes the value p i p wf (1) p wf * When, it is calculated using formula (2):

[0109] ψ(p i = 46220.42 MPa 2 / mPa·s、ψ(p wf (1))=27389.40 MPa 2 / mPa·s、ψ(p wf * = 7119.02 MPa 2 / mPa·s; calculated using formula (4): S p (i) = 6.68;

[0110] Step 2: Calculate the start time t of the decreasing phase * ;

[0111] (1) Set the production time t range to [1, t] T ]; where: according to Table 1, the target production time t T =500 d;

[0112] (2) The production time t increases from 1 to the target production time t. T The corresponding result is obtained by formula (6). The calculation results are shown below. Figure 2 The corresponding mean formation pressure is calculated using formula (11). The calculation results are shown below. Figure 2 Drawing the mass balance equation curve;

[0113] (3) The production time t increases from 1 to the target production time t. T The result is obtained by formula (7). The calculation results are shown below. Figure 3 Let ψ(p) take the following values: The corresponding average formation pressure is calculated using formula (3). The calculation results are shown below. Figure 3 ; Drawing the capacity equation curve;

[0114] (4) The mass balance equation Curve and capacity equation The curves are drawn together Figure 4 The x-axis corresponding to the intersection of the curves is the start time t of the decline phase of the gas well. * It can be seen that the starting time t of the decreasing phase * =472d;

[0115] Step 3: Determine the target production time t T With the start time t of the decreasing phase * Relationship;

[0116] Target production time t T =500d; Decreasing phase start time t * = 472d; Target production time t T =500d > the start time of the decreasing phase t * =472d; indicating the target production time t T In the decreasing phase; proceed to step 4;

[0117] Step 4: Calculate the gas production q during the decline phase. sc (t);

[0118] (1) Let t = the start time of the decreasing phase t * =472d;

[0119] (2) Calculate the gas production q at time t. sc (t);

[0120] ① Assume the initial value of the iteration is q sc (t) B =60000m 3 / d;t=t * =472d, therefore G p (t-1)=60000×472=28320000m 3 ;

[0121] ② The corresponding formula is obtained by calculation using formula (8).

[0122] The corresponding mean formation pressure is calculated using formula (11).

[0123] ③ Let p take a value Using formula (2), the corresponding result is calculated.

[0124] ④ Substituting into formula (9), the final value q of the iteration is calculated. sc (t) E =59854.15m 3 / d;

[0125] ⑤ Determine the initial value q for iteration sc (t) B With the final value q of the iteration sc (t) E The iteration error and upper limit of error ε(q) sc The relationship between )

[0126] |q sc (t) B -q sc (t) E | / q sc (t) E =0.24% > ε(q) sc =0.1%, see Table 1; does not satisfy formula (10); then let

[0127] q sc (t) B =q sc (t) E =59854.15m 3 / d Repeat steps 2 through 5 to continue iterating.

[0128] The iterative process continues as follows:

[0129] ②The corresponding formula is obtained by using formula (8).

[0130] The corresponding mean formation pressure is calculated using formula (11).

[0131] ③ Let p take a value Using formula (2), the corresponding result is calculated.

[0132] ④ Substituting into formula (9), we obtain the final value q of the iteration. sc (t)E =59854.32m 3 / d;

[0133] ⑤ Determine the initial value q for iteration sc (t) B With the final value q of the iteration sc (t) E The iteration error and upper limit of error ε(q) sc The relationship between )

[0134] |q sc (t) B -q sc (t) E | / q sc (t) E =0.00% < ε(q) sc The percentage 0.1% satisfies formula (10);

[0135] Iteration ended;

[0136] ⑥ Determine the target production time t T Relationship with production time t;

[0137] Production time t = 473 days < target production time t T =500d; Enter (3);

[0138] (3) Increment t by 1 to get the new t, that is, let t = t + 1, and iterate through step (2) to calculate the gas production q at that moment. sc (t);

[0139] ① Assume the initial value of the iteration is q sc (t) B equals 60000m 3 / d;

[0140] ② The corresponding formula is obtained by calculation using formula (8). The corresponding mean formation pressure is calculated using formula (11).

[0141] ③ Let p take a value The corresponding formula (2) is used to calculate the result.

[0142] ④ Substituting into formula (9), the final value q of the iteration is calculated. sc (t) E ;

[0143] ⑤ Determine q sc (t) B With q sc (t) EDoes the iteration error between them satisfy equation (10)?

[0144] The detailed iterative calculation process is drawn as follows Figure 5 ; Figure 5 (a) shows the calculation process for the first iteration at each time point. Figure 5 (b) shows the calculation process for the second iteration at each time point; after two iterations, the iteration error requirement is met at each calculation point. When the production time t = 500 days, the requirement t = t is met. T The calculation is complete, output q. sc (t)=q sc (t) E =57990.77m 3 / d.

[0145] When t = t T When d = 500, the numerical simulation yields q sc (t T ) = 56893.1m 3 / d, q calculated in this invention sc (t T ) = 57990.77m 3 / d, the absolute value of the relative error between the two is 1.93%, indicating that the present invention has high precision.

[0146] To further verify the reliability of the invention over a longer time range, the production time t of well m29-4 was set from 1 to 1000 days, with the target production time t... T The value of t increases sequentially from 1d to 1000d, and the present invention is used to calculate each t. T The corresponding q sc (t T The calculation results are shown below. Figure 6 This indicates that the present invention has different target production times t T It always maintains high precision.

Claims

1. A method for predicting a target gas production rate of a naturally declining gas well, the method comprising: The method is as follows: ​ Step 1: Calculate the pseudo-pressure ψ(p) and the initial value of the pressure-skin S p (i); Through the following formula (2) where: ψ(p) is the pseudo-pressure corresponding to the pressure p, MPa 2 / mPa·s; a is μ(p)Z(p)-p 2 First coefficient obtained by linear fitting of the curve, dimensionless b is μ(p)Z(p) - p 2 Second coefficient obtained from linear fit of the curve, dimensionless p is pressure, MPa; p0 is reference pressure, MPa; μ(p) is the gas viscosity corresponding to the pressure p, mPa·s; Z(p) is the deviation factor corresponding to the pressure p, dimensionless; when p takes the value p i , p wf (1), p wf * , the pseudo-original formation pressure ψ(p i ), the pseudo-well bottom flow pressure ψ(p wf (1)), the pseudo-well bottom flow pressure ψ(p wf (1)) when p takes the value p wf * , the pseudo-well bottom flow pressure ψ(p wf * ) when p takes the value p calculating the initial value S of the pressure conversion skin p (i); Through the following formula (4) where: S p (i) is the initial value of the pressure conversion skin, dimensionless; p sc Standard pressure, MPa; Z sc s is the standard deviation coefficient, dimensionless; T sc T is the standard temperature, K; T is the reservoir temperature, K; K is the reservoir permeability, 10 -3 μm 2 ; h is the reservoir thickness, m; ψ(p i ) is the pseudo-initial formation pressure, MPa 2 / mPa·s; p i P is the original formation pressure, MPa; ψ(p wf (1)) is the pseudo-bottom-hole flowing pressure, MPa wf (1) is the pseudo-bottom-hole flowing pressure, MPa 2 / mPa·s; p wf (1) bottom hole flowing pressure for t = 1, MPa; q sc (1) Wellhead gas production rate for t = 1, m3 / d 3 / d; The initial value S of the pressure conversion skin is calculated p (i); Step 2: Calculate the decreasing phase start time t * ; (1) setting the t value range as [1, t T ]; where t is the production time, d;t T is the target production time, d;t * is the start time of the decreasing phase, d; (2) Average formation pressure is calculated using material balance The value of production time t is increased from 1 to the target production time t T by the following equation (6) wherein: Pavg(t) is the average formation pressure at time t, MPa; Z r (t) is corresponding bias coefficient, dimensionless; Z i For p i Corresponding bias coefficient, dimensionless; G is the gas well controlled reserves, m 3 ; q sc * For the stable production phase, the gas production rate, m 3 / d; The corresponding By the following equation (11) wherein: A is The first coefficient, dimensionless, obtained by linear fitting of the curve. B is the second coefficient obtained from a linear fit of the curve, dimensionless; The corresponding average formation pressure is calculated Plotting the material balance equation curve; (3) The average formation pressure is calculated using the productivity equation The value of the production time t is increased from 1 to the target production time t T by the following equation (7) wherein: Pavg(t) = pseudo-average formation pressure at time t, MPa 2 / mPa·s; ψ(p wf * ) is the pseudo bottom hole flowing pressure, MPa wf * when p 2 / mPa·s; p wf * Pwf for the decline phase, MPa; t D t is the production time, t D = t / 1, t D > 0, dimensionless; The calculated pseudo-average formation pressure at the corresponding time Let the expression (3) be Let the expression (3) be By the following expression (3) The corresponding average formation pressure is calculated The productivity equation is plotted curve; (4) Acquire the start time t of the decreasing phase * The mass balance equation Curve and capacity equation When the curves are plotted on a graph, the x-axis corresponding to the intersection of the two curves represents the start time t of the decline phase of the gas well. * ; Step 3: Determine target production time t T in relation to the start time t * of the decreasing phase. If the target production time t T is reached * , then the target production time t T at this moment is set to t sc = t T - t sc * , and the calculation ends.

2. The method according to claim 1, characterized in that: If the target production time t T ≥ the start time of the decreasing phase t * , the target production time t T is located in the decreasing phase; further comprising: Step 4: Calculate the gas production rate q in the decline phase sc (t); (1) Let production time t = time of start of decreasing phase t * ; (2) Calculate the gas production q at time t sc (t); 1. The initial value of the iteration of the gas production rate q sc (t) B , the iteration of the initial value q sc (t) B is in the range [1, q sc * ] ② Through the following formula (8) wherein: q sc (t) B is the iteration initial value of the gas production rate in the decline phase, m 3 / d; G p Cumulative gas production at time t-1, m 3 ; The corresponding The corresponding average formation pressure is calculated by equation (11) iii. Let p in equation (2) take the value By equation (2), the corresponding pseudo-average formation pressure is calculated (4) the pseudo-average formation pressure is calculated is substituted into the following equation (9) wherein: q sc (t) E is the final value of the iteration of the gas production rate in the decline phase, m 3 / d; The iteration final value of the gas production quantity q is calculated sc (t) E ; (5) determining whether the iteration error between the iteration initial value q sc (t) B and the iteration final value q sc (t) E satisfies the following equation (10) |q sc (t) B -q sc (t) E | / q sc (t) E ≤ε(q sc ) (10) where: |q sc (t) B -q sc (t) E | / q sc (t) E is the iteration error, dimensionless. ε(q sc ) is the upper limit of the error of the iterative calculation, 0 < ε(q sc ) < 10%, dimensionless; If satisfied, let q sc (t) = q sc (t) E , directly execute ⑥; If not, let q sc (t) B = q sc (t) E , repeat ① to ⑤ to continue iteration; until the iteration error satisfies formula (10), output q sc (t) = q sc (t) E , execute ⑥; ⑥determining the relationship between the production time t and the target production time t T ; If production time t = target production time t T , output q sc (t T ) = q sc (t), calculation ends; If production time t < target production time t T , execute (3); (3) increase t by 1 as a new t, i.e. let t = t + 1, and iterate through step (2) to calculate the gas production q at this moment sc (t), until the gas production q sc (t) at this moment meets the iteration error requirement, and the production time t = target production time t T is met, and output q sc (t T ) = q sc (t), and the calculation is completed.

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