A method for predicting target decline time of a constant volume closed gas well

Abstract

This invention relates to the field of oil and gas field development technology, specifically to a method for predicting the target decline time of a constant-volume closed gas well. The method comprises the following steps: Step 1: Setting the target production rate, the set known production time, and the gas production corresponding to the known production time; Step 2: Calculating the initial values ​​of the simulated bottomhole flowing pressure and the pressure conversion skin; Step 3: Setting the production time equal to the set known production time; Step 4: Iteratively calculating the wellhead gas production at time t+1; Step 5: Iteratively calculating the wellhead gas production at time t+1; Step 6: Calculating the target decline time. This invention establishes a method for predicting the target decline time of a gas well, employing an iterative solution approach to achieve the prediction of the target decline time. This addresses the practical needs faced during gas well production and is of great significance for gas field development.

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 decline time of a constant-volume closed gas well. Background Technology

[0002] Research on gas well decline includes decline rate, decline fraction, and decline time. The foundation of decline research includes basic decline models such as exponential decline, hyperbolic decline, and harmonic decline. Bottom hole flowing pressure is an important indicator of the characteristics of gas well decline, but basic decline models do not directly consider the influence of bottom hole flowing pressure on decline. When used to interpret decline laws, they usually exhibit multiple solutions. If used to predict decline time, the prediction results will also exhibit multiple solutions and high errors. Other decline models based on basic decline models are also constrained by multiple solutions.

[0003] When a gas well enters its decline phase, a common practical need is to determine how long it will take for production to decrease to a certain level. Since existing prediction methods are prone to multiple interpretations, developing an effective method for predicting decline time is of significant practical value 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 decline time of a constant-volume closed gas well.

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

[0006] For constant-volume gas-driven wells, after entering the decline phase, the full-stage productivity equation is:

[0007]

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

[0009] t is the production time, t≥t * ,d;

[0010] t * The decremental production start time for gas wells is d;

[0011] Let be the average formation pressure at time t, in MPa;

[0012] ψ(p wf (t) represents the pseudo-bottomhole flowing pressure at time t, in MPa. 2 / mPa·s;

[0013] p wf (t) represents the bottom hole flowing pressure at time t, in MPa;

[0014] p sc Standard pressure, MPa;

[0015] Z sc The standard deviation coefficient is dimensionless.

[0016] T sc Standard temperature, K;

[0017] T is the reservoir temperature, in K;

[0018] K is the reservoir permeability, 10 -3 μm 2 ;

[0019] h is the reservoir thickness, in meters;

[0020] q sc (t) represents the wellhead gas production at time t, in m 3 / d;

[0021] r e Let vent radius be m;

[0022] r w Let be the radius of the wellbore, in meters (m).

[0023] S p (t) represents the pressure change at time t, dimensionless.

[0024] Among them, pressure conversion skin S p The independent approximate solutions of (t) are:

[0025]

[0026]

[0027] In the formula: S p (i) represents the initial value of the pressure conversion skin, which is dimensionless;

[0028] μ i For p i The corresponding gas viscosity, mPa·s;

[0029] p i The original formation pressure is expressed in MPa.

[0030] μ wf (t) is p wf (t) corresponds to the gas viscosity in mPa·s;

[0031] t D For dimensionless production time, t D = t / 1, requiring t D >0, dimensionless;

[0032] ψ(p i () represents the pseudo-original formation pressure, in MPa 2 / mPa·s;

[0033] ψ(p wf (1) is p wf (1) Simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0034] p wf (1) is the bottom hole pressure at t=1, in MPa;

[0035] q sc (1) is the wellhead gas production at t=1, m 3 / d.

[0036] Substituting equation (2) into equation (1), the independent approximate solution of the pressure conversion skin allows the full-stage production capacity equation to be freed from the vent radius r. e The influence of gas viscosity μ at different times also exists. wf To further improve the computational convenience of the capacity equation, and considering the impact of computational accuracy on the capacity equation, an independent solution for the pressure conversion skin is proposed:

[0037]

[0038] Substituting equation (4) into equation (1), the independent solution of the pressure conversion skin allows the full-stage production capacity equation to be freed from the vent radius r. e Gas viscosity μ wf The effect of (t) is obtained:

[0039]

[0040] The formula for calculating the pseudo-pressure ψ(p) is:

[0041]

[0042] In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p, in MPa 2 / mPa·s;

[0043] p represents pressure, in MPa;

[0044] p0 is the reference pressure, with a value of 0, MPa;

[0045] a is μ(p)Z(p)-p 2 The curve is obtained by linear fitting, and the first coefficient is dimensionless.

[0046] b is μ(p)Z(p)-p 2The curve uses the second coefficient obtained through linear fitting, which is dimensionless.

[0047] μ(p) is the gas viscosity corresponding to p, in mPa·s;

[0048] Z(p) is the deviation coefficient corresponding to p, which is dimensionless;

[0049] If at t * At time t, the gas well enters a decreasing phase; the bottom hole flowing pressure during this decreasing phase is p. wf * The bottom hole pressure remains constant, i.e., p wf (t)=p wf * = constant, substituting into equation (1), we can derive the expression for the decreasing output at time t:

[0050]

[0051] In the formula: ψ(p) wf * ) represents the bottom hole flowing pressure p wf * Corresponding simulated bottom hole flowing pressure, MPa 2 / mPa·s;

[0052] p wf * To reduce the bottom hole flowing pressure during production, in MPa;

[0053] At time t, the mass balance equation for a constant-volume gas-driven well is:

[0054]

[0055] In the formula: Z r (t) is The corresponding deviation coefficient is dimensionless.

[0056] Z i For p i The corresponding deviation coefficient is dimensionless.

[0057] G represents the controlled reserves of the gas well, m 3 ;

[0058] G p (t) represents the cumulative gas production at time t, m 3 .

[0059] At t+1, the expression for decreasing production is:

[0060]

[0061] In the formula: q sc (t+1) represents the wellhead gas production at time t+1, m3 / d;

[0062] The pseudo-average formation pressure at t+1, in MPa 2 / mPa·s;

[0063] The mean formation pressure at time t+1, in MPa;

[0064] (t+1) D Let (t+1) be the dimensionless production time corresponding to t+1. D = (t+1) / 1, dimensionless.

[0065] At time t+1, the mass balance equation for a constant-volume gas-driven well is:

[0066]

[0067] In the formula: Z r (t+1) is The corresponding deviation coefficient is dimensionless.

[0068] It can be seen that: if G p If t is known, then both equations (6) and (7) contain unknowns. q sc (t+1) can be obtained iteratively. and q sc (t+1);

[0069] The specific process of iterative solution:

[0070] (1) Assume the initial value of the wellhead gas production at time t+1 is q. sc (t+1) B q sc (t+1) B The value range of q is [10000, 100000]; let q sc (t+1)=q sc (t+1) B Substituting into equation (11) yields the following result.

[0071]

[0072] In the formula: q sc (t+1) B Let m be the initial value of the wellhead gas production at time t+1. 3 / d;

[0073] (2) The result obtained from equation (11) Substituting into equation (12), the iterative final value q of the wellhead gas production at time t+1 is calculated. sc (t+1) E :

[0074]

[0075] In the formula: q sc (t+1) E Let m be the iterative final value of the wellhead gas production at time t+1. 3 / d;

[0076] (3) Determine the initial value q of the wellhead gas production at time t+1. sc (t+1) B The iterative final value q of the wellhead gas production at time t+1 sc (t+1) E Does it meet the following requirements:

[0077]

[0078] In the formula: ε(q sc ) represents the upper limit of error for iterative calculation, 0 ≤ ε(q) sc ≤10%, dimensionless;

[0079] ① If equation (13) is satisfied, then output q. sc (t+1)=q sc (t+1) E ;

[0080] ②If equation (13) is not satisfied, then let q sc (t+1) B =q sc (t+1) E Repeat the above steps until equation (13) is satisfied, and then output q. sc (t+1)=q sc (t+1) E .

[0081] During the decline production process of a gas well, t is usually known. 0 q at time sc (t 0 ) and other parameters, when the gas production rate is q sc (t 0 Decrease to target output q sc (t T When ), the corresponding target decrease time t T Usually unknown. Target decrease time t T The solution can be obtained through iterative steps. The specific process for iterative solution is as follows:

[0082] (1) Let t = t0 Using equations (11), (12), and (13), the q at this point is obtained through iterative calculation. sc (t+1)=q sc (t 0 +1), determine if q is satisfied. sc (t+1)≤q sc (t T If the condition is met, the calculation stops; otherwise, the iteration proceeds to the next time step t.

[0083] (2) Let t = t 0 +1, using equations (11), (12), and (13), q is obtained through iterative calculation. sc (t+1)=q sc (t 0 +2), determine whether q is satisfied. sc (t+1)≤q sc (t T If the condition is met, the calculation stops; otherwise, the iteration proceeds to the next time step t.

[0084] (3) Let t = t 0 +2, repeat the above steps until the calculated q is obtained at a certain time t. sc (t+1) satisfies q sc (t+1)≤q sc (t T Stop iterative calculations;

[0085] (4) Calculate t and q sc Substituting (t+1) into the following formula, we can calculate the target decrease time t. T :

[0086]

[0087] In the formula: t T The time for the target to decrease is d;

[0088] q sc (t T ) represents the target output, q sc (t T )≤q sc (t 0 ), m 3 / d;

[0089] q sc (t 0 ) for t 0 Gas production at any given time, m 3 / d;

[0090] t 0is the set known production time, d;

[0091] In formula (14): When q sc (t + 1) = q sc T , t T = t; When q sc (t + 1) < q sc T , t T < t; Therefore, formula (11) is normalized.

[0092] The technical effect of the present invention is as follows:

[0093] The present invention establishes a method for predicting the target decline time of a gas well. By using the method of successive iteration to solve, the prediction of the target decline time is achieved, which solves the actual needs faced in the production process of gas wells and is of great significance for gas field development. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 is the gas production of Well A.

[0095] Figure 2 is the bottom-hole flowing pressure of Well A.

[0096] Figure 3 is the first successive iteration diagram.

[0097] Figure 4 is the second successive iteration diagram.

[0098] Figure 5 is q sc (t + 1) ≤ q sc (t T ) judgment diagram. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] A method for predicting the target decline time of a constant-volume closed gas well is as follows:

[0100] Step 1: Set the target production q sc (t T ), satisfying q sc (t T ) ≤ q sc (t 0 );

[0101] Set t 0 = t * , t 0 ≥ t * , q sc (t 0 ) = 114085 m 3 / d;

[0102] Step 2: Put p i p wf (1) p wf * Substituting these values ​​into equation (6), the pseudo-pressure and pseudo-original formation pressure ψ(p) are calculated. i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1) Bottom-hole flowing pressure p wf * The corresponding pseudo-bottom hole flowing pressure ψ(p) wf * );

[0103] The initial value S of the pressure conversion skin is calculated using formula (3). p (i);

[0104] Step 3: Let t = t 0 ; t≥t * ;

[0105] Step 4: Iteratively calculate the wellhead gas production at time t+1.

[0106] (1) Assume the initial value of the wellhead gas production at time t+1 is q. sc (t+1) B q sc (t+1) B The value range of q is [10000, 100000]; let q sc (t+1)=q sc (t+1) B The average formation pressure at t+1 is calculated using formula (11).

[0107] (2) The result obtained from equation (11) Substituting into equation (6), we obtain the following calculation:

[0108] (3) Substituting into formula (12), the iterative final value q of the wellhead gas production at time t+1 is calculated. sc (t+1) E ;

[0109] (4) Determine the initial value q of the wellhead gas production at time t+1. sc (t+1) B The iterative final value q of the wellhead gas production at time t+1 sc (t+1) E Does it satisfy formula (13)?

[0110] ① If equation (13) is satisfied, then output q. sc(t+1)=q sc (t+1) E Enter (5);

[0111] ②If equation (13) is not satisfied, then let q sc (t+1) B =q sc (t+1) E Repeat steps (1)-(4) in step 4 until equation (13) is satisfied, and then output q. sc (t+1)=q sc (t+1) E (5) Determine whether q is satisfied at this time. sc (t+1)≤q sc (t T );

[0112] (5) Determine whether q is satisfied at this time. sc (t+1)≤q sc (t T );

[0113] ① If satisfied, output q. sc (t+1), proceed to step 6;

[0114] ②If not satisfied, proceed to step 5;

[0115] Step 5: Calculate q iteratively sc (t+1);

[0116] Increment t by 1 each time, then return to step 4 to iteratively calculate q. sc (t+1), until q is satisfied. sc (t+1)≤q sc (t T Output q sc (t+1), proceed to step 6;

[0117] Step 6: Calculate the target decrease time t T ;

[0118] The calculated t and q sc Substituting (t+1) into formula (14), we can calculate the target decrease time t. T . Specific Implementation

[0120] Well A is a gas well in numerical simulation. The basic parameters of Well A are shown in Table 1, and the gas production is shown in... Figure 1 ;

[0121] Table 1 Basic parameters of well A

[0122]

[0123] Bottom-hole flowing pressure Figure 2 It can be seen that well A begins to decrease from day 501, therefore t * =501d. The present invention is used to calculate q. sc (t T The corresponding target decrease time t T The calculation process is as follows, and the results are verified.

[0124] A method for predicting the target decline time of a constant-volume closed gas well is as follows:

[0125] Step 1: Set the target output q sc (t T ) = 50000m 3 / d, satisfying q sc (t T )≤q sc (t 0 );

[0126] Set t 0 =t * =501d, satisfying t 0 ≥t * , then q sc (t 0 )=114085m 3 / d;

[0127] Step 2: Calculate the initial values ​​of the simulated bottom hole flowing pressure and the pressure conversion skin;

[0128] p i p wf (1) p wf * Substituting the values ​​into equation (6) respectively, we can calculate the results.

[0129] ψ(p i = 46220.42MPa 2 / mPa·s

[0130] ψ(p wf (1))=36756.48MPa 2 / mPa·s

[0131] ψ(p wf * ) = 1824.26 MPa 2 / mPa·s;

[0132] The initial value S of the pressure conversion skin is calculated using formula (3). p (i) = 6.72;

[0133] Step 3: Let t = t 0=501d;

[0134] Step 4: Iteratively calculate the wellhead gas production q at time t+1. sc (t+1);

[0135] (1) Assume the initial value of the wellhead gas production at time t+1 is q. sc (t+1) B =30000m 3 / d, satisfying q sc (t+1) B The value range of q is [10000, 100000]; let q sc (t+1)=q sc (t+1) B Substituting into equation (11) yields the following result.

[0136] (2) The calculated Substituting into equation (6), we get:

[0137] (3) Substituting into equation (12), the iterative final value q of the wellhead gas production at time t+1 is calculated. sc (t+1) E =88181.79m 3 / d;

[0138] (4) Determine the initial value q of the wellhead gas production at time t+1. sc (t+1) B The iterative final value q of the wellhead gas production at time t+1 sc (t+1) E Does it satisfy the following formula (13)?

[0139] Calculated Due to ε(q) sc ) = 0.1%, at this time q sc (t+1) B With q sc (t+1) E Since equation (13) is not satisfied, let q sc (t+1) B =q sc (t+1) E =88181.79m 3 / d, repeat steps (1)-(4) in step 4;

[0140] Repeat step (1) to calculate:

[0141] Repeat step (2) to calculate:

[0142] Repeat step (3) to calculate: q sc (t+1) E =88112.83m 3 / d;

[0143] Repeat step (4) to calculate: Due to ε(q) sc ) = 0.1%, therefore q at this time sc (t+1) B With q sc (t+1) E Equation (13) is satisfied, therefore the output q is obtained. sc (t+1)=q sc (t+1) E =88112.83m 3 / d, enter (5);

[0144] (5) Due to q sc (t T ) = 50000m 3 / d, at this time q sc (t+1)=88112.83m 3 / d, we can determine: q at this time sc (t+1) does not satisfy q sc (t+1)≤q sc (t T Proceed to step 5;

[0145] Step 5: Calculate q iteratively sc (t+1);

[0146] Increment t by 1 each time, then return to step 4 to iteratively calculate q. sc (t+1), until a certain time t is obtained by calculating q sc (t+1) satisfies q sc (t+1)≤q sc (t T Stop iterative calculations;

[0147] The iterative calculation process and results are shown in [link to calculation]. Figure 3 , Figure 4 and Figure 5 The details are as follows:

[0148] (1) Figure 3 This is the calculation process for the first iteration, with an initial value q. sc (t+1) B All are assumed to be 30000m 3 / d, the relative error of the first successive iteration is greater than 0.1%, which does not satisfy equation (13), so the second successive iteration is performed;

[0149] (2) Figure 4 This is the calculation process for the second successive iteration, with the initial value q. sc (t+1) B All are equal to the final value of the first iteration, and the relative error of each iteration in the second iteration is less than or equal to 0.1%, all satisfying equation (13).

[0150] (3) Figure 5 To determine the q calculated at each time t sc Does (t+1) satisfy q? sc (t+1)≤q sc (t T ), that is, whether q is satisfied. sc (t+1)-q sc (t T )≤0, when t=998d sc (t+1)=50038.90m 3 / d, when t=999d, q sc (t+1)=49987.07m 3 / d, therefore, the q calculated when t=1000d is obtained sc (t+1) satisfies q sc (t+1)≤q sc (t T At this point, the iterative calculations stop.

[0151] Step 6: Calculate the target decrease time t T ;

[0152] The t and q obtained from successive iterations sc Substituting (t+1) into formula (14), the target decrease time t is calculated. T =999.75d.

[0153] Numerical simulation results show that when t = 1016d, q sc (t+1)=50018.6m 3 / d, when t=1017d, q sc (t+1)=49968.7m 3 / d, meaning when gas well production decreases to the target production of 50,000 m³. 3 / d, the actual production time t is between 1016 and 1017 days.

[0154] Based on the 1016d and 1017d obtained from numerical simulation, and the t calculated in this invention... TWhen compared with 999.75d, the results show that the absolute value of the relative error is between 1.70% and 1.79%, indicating that the calculation results of this invention have high accuracy.

Claims

1. A method for predicting the target decline time of a constant-volume closed gas well, characterized in that: The method is as follows: Step 1: Set q sc (t T ), q sc (t 0 ) and t 0 ; Where: q sc (t T ) represents the target output, q sc (t T )≤q sc (t 0 ); q sc (t 0 ) for t 0 Gas production at any given moment; t 0 Given a known production time, t 0 ≥t * ; Step 2: Calculate the initial values ​​S of the simulated bottom hole flowing pressure and pressure conversion surface. p (i) The pseudo-original formation pressure ψ(p) is calculated using the following formula (6). i ), p wf (1) The pseudo-bottom flow pressure ψ(p) wf (1) Bottom-hole flowing pressure p wf * The corresponding pseudo-bottom hole flowing pressure ψ(p) wf * ): (6) In the formula: ψ(p) is the pseudo-pressure corresponding to pressure p; p represents pressure; p0 is the reference pressure, with a value of 0; a is μ(p)Z(p)-p 2 The curve is obtained using the first coefficient obtained through linear fitting; b is μ(p)Z(p)-p 2 The curve uses the second coefficient obtained through linear fitting; μ(p) is the gas viscosity corresponding to p; Z(p) is the deviation coefficient corresponding to p; The initial value S of the pressure conversion skin is calculated using the following formula (3). p (i): (3) In the formula: S p (i) represents the initial value of the pressure conversion skin; ψ(p i ) represents the pseudo-original formation pressure; p i This represents the original formation pressure; Z sc The standard deviation coefficient; T sc Standard temperature; p sc Standard pressure; K is the reservoir permeability; h is the reservoir thickness; T is the reservoir temperature; ψ(p wf (1) is p wf (1) The simulated bottom hole flowing pressure; p wf (1) is the bottom hole flowing pressure at t=1; q sc (1) is the wellhead gas production at t=1; Step 3: Let t = t 0 ; t≥t * ; Where t is the production time; since t 0 ≥t * Therefore, t≥t is satisfied. * ;t * The time when a gas well begins to decrease production; Step 4: Iteratively calculate the wellhead gas production at time t+1 (1) Assume the initial value of the wellhead gas production at time t+1. , The value range of is [10000, 100000]; let Substituting into equation (11), the average formation pressure at time t+1 is calculated. : (11) In the formula: The average formation pressure at time t+1; Z r (t+1) is The corresponding deviation coefficient; p i This represents the original formation pressure; Z i For p i The corresponding deviation coefficient; G represents the controlled reserves of the gas well; G p (t) represents the cumulative gas production at time t; q sc (t+1) B This is the initial value for the wellhead gas production at time t+1. (2) The result obtained from equation (11) Substituting into equation (6), we obtain the following calculation: ; (3) Substituting into equation (12), the iterative final value q of the wellhead gas production at time t+1 is calculated. sc (t+1) E : (12) In the formula: q sc (t+1) E This represents the iterative final value of the wellhead gas production at time t+1. The pseudo-average formation pressure at t+1; ψ(p wf * ) represents the bottom hole flowing pressure p wf * Corresponding pseudo-bottomhole flowing pressure; p wf * To reduce the bottom hole pressure during production, the bottom hole pressure is kept constant during production reduction. (t+1) D Let (t+1) be the dimensionless production time corresponding to t+1. D =(t+1) / 1; (4) Determine the initial value of the wellhead gas production at time t+1. The final value of the iterative wellhead gas production at t+1 Does it satisfy the following formula (13)? ① If equation (13) is satisfied, then the output is... , enter (5); ②If equation (13) is not satisfied, then let Repeat steps (1)-(4) in step 4 until equation (13) is satisfied, and then output the result. ; (13) In the formula: ε(q sc ) represents the upper limit of error for iterative calculation, 0 ≤ ε(q) sc ≤10%; (5) Determine whether the condition is met at this time. ; ① If satisfied, output q. sc (t+1), proceed to step 6; ② If not satisfied, proceed to step 5; Step 5: Calculate q iteratively sc (t+1); Increment t by 1 each time, then return to step 4 to iteratively calculate q. sc (t+1), until the condition is met. Output q sc (t+1), proceed to step 6; Step 6: Calculate the target decrease time t T ; The calculated t and Substituting into the following formula, the target decrease time t is calculated. T : (14) In the formula: t T Decrease the time to the target.

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