A method for predicting the production decline rate of gas wells in a constant-volume closed gas reservoir

Abstract

The present invention belongs to the technical field of gas reservoir engineering, and particularly relates to a method for predicting the gas production decline rate of gas wells in a constant-volume closed gas reservoir. Take D(n) as the initial value of the decline rate, and obtain the annual gas production △G in the first year after decline p1 (n); take the initial formation pressure P at the end of the first year after the decline of the gas well R1 m‑1 (n), and require P R1 m‑1 (n) < P Ri , and obtain the initial deviation coefficient Z R1 m‑1 (n), and obtain the formation pressure P in the first year after decline R1 m (n); calculate the daily gas production q1(n) at the end of the first year after decline; calculate the gas well decline rate D′(n). By adopting the ratio of gas production at different times, the present invention eliminates the influence of parameters and greatly improves the calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of gas reservoir engineering, and particularly relates to a method for predicting the production decline rate of gas wells in a constant-volume closed gas reservoir. Background Technique

[0002] The production decline law of gas wells is one of the important indicators for the dynamic analysis of gas well production. Especially for tight reservoirs, most of the production time of gas wells is in the decline period, and about 50% of the recoverable reserves are produced during the decline period. Therefore, the production decline law is of great significance for the dynamic prediction of gas fields.

[0003] At present, the production decline of gas wells is mainly fitted by the Arps decline formula to obtain the decline rate and decline index of gas wells. This method is only applicable to gas wells entering the decline period and cannot predict the decline rate of gas wells during the stable production stage of gas wells. At present, the decline rate of gas wells can only be predicted by numerical simulation methods. However, for tight reservoirs, there are many gas wells, the numerical simulation workload is huge, a large number of static and dynamic parameters are required, and there are multiple solutions, which is difficult to apply in the field. Summary of the Invention

[0004] In view of the general exponential decline characteristics of constant-volume closed gas reservoirs, the present invention combines the pseudo-steady state gas well productivity formula, the material conservation equation, and the exponential decline formula to establish a method for predicting the production decline rate of gas wells.

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

[0006] (1) For a constant-volume closed gas reservoir, the decline of gas wells generally conforms to the exponential decline model. The gas production at any time j during the decline period of the gas well is:

[0007]

[0008] Where: q j is the daily gas production at time j, m 3 / d; q i is the daily gas production during the stable production period, m 3 / d;

[0009] t j is the time at time j during the decline period, d; t 0 is the time at the end of the stable production period, d;

[0010] D is the decline rate of the gas well, d -1 ;

[0011] Therefore, the decline rate D of the gas well is:

[0012]

[0013] For the decline period of the gas well, only the gas production q at time j needs to be obtained jThe decline rate D of the gas well can be obtained, and the production can be calculated through the productivity formula.

[0014] (2) For a constant-volume closed gas reservoir, after the gas well produces at a constant production rate for a period of time, the gas well reaches a pseudo-steady state, and the gas well productivity equation is:

[0015]

[0016] In the formula: q is the daily gas production of the gas well, m 3 / d; k is the effective permeability of the gas reservoir, mD; h is the effective thickness of the gas reservoir, m; T is the gas reservoir temperature, K; μ g is the natural gas viscosity, mPa·S; Z R is the deviation coefficient corresponding to P R r, dimensionless; r e is the drainage radius, m; r w is the wellbore diameter, m; S is the total skin factor, dimensionless; P R is the formation pressure, MPa; P wf is the bottom-hole flowing pressure, MPa;

[0017] When the production declines, that is, when producing at a constant bottom-hole flowing pressure, the production q at any time j j is

[0018]

[0019] In the formula: P Rj is the formation pressure at time j, MPa; μ gj is the natural gas viscosity corresponding to P Rj Z, dimensionless; P Rj is the deviation coefficient corresponding to P Rj P, dimensionless; P wfb is the lowest bottom-hole flowing pressure, MPa;

[0020] Since the effective permeability k of the gas reservoir in the gas well productivity equation is affected by many factors such as experimental accuracy, logging interpretation model, and reservoir heterogeneity, the error is generally large, and it is difficult to obtain the total skin factor S, resulting in a large error in calculating the gas well production by the gas well productivity equation. In the present invention, in the form of the production ratio, the influence of the two parameters is removed, greatly improving the calculation accuracy; the production ratio at time j and time j-1 is:

[0021]

[0022] In the formula: q j-1 is the daily gas production at time j-1, m 3 / d; P R(j-1) is the formation pressure at time j-1, MPa; μ g(j-1) is the natural gas viscosity corresponding to P R(j-1)Corresponding natural gas viscosity, mPa·S; Z R(j-1) is P R(j-1) Corresponding deviation factor, dimensionless;

[0023] When t j-1 = t 0 At that time, the daily gas production q at time j j Can be calculated using the daily gas production q during the stable production period i And the formation pressure P at the end of the stable production period Ri Calculation:

[0024]

[0025] In the formula: P Ri Is the formation pressure at the end of the stable production period, MPa; μ gi Is P Ri Corresponding natural gas viscosity, mPa·S; Z Ri Is P Ri Corresponding deviation factor, dimensionless;

[0026] For a certain gas well that has been produced, the natural gas deviation factor and viscosity can be obtained by interpolation based on high-pressure physical property experimental data. The daily gas production q during the stable production period i Is known, the minimum bottom-hole flowing pressure P wfb And the formation pressure P at the end of the stable production period Ri Are easy to obtain. Therefore, the key parameter for calculating the daily gas production q at time j j Is the formation pressure P at time j Rj .

[0027] (3) According to the material balance equation, for a constant-volume closed gas reservoir, P R / Z R ~G p Show a linear relationship:

[0028]

[0029] In the formula: P i Is the original formation pressure, MPa; Z i Is P i Corresponding natural gas deviation factor, dimensionless; G p Is the cumulative gas production of the gas well, m 3 ; G is the dynamic reserve of the gas well, m 3 ;

[0030] Therefore, the relationship between pressure and cumulative gas production between any two moments is as follows:

[0031]

[0032] In the formula: Is the cumulative gas production from time j - 1 to time j, m3 ;

[0033] When t j-1 = t 0 , it is the cumulative gas production ΔG from the end of the stable production period to the j-th moment pj ; Therefore, the formation pressure P at the j-th moment Rj is:

[0034]

[0035] In the formula: ΔG pj is the cumulative gas production from the end of the stable production period to the j-th moment, m 3 ;

[0036] Since the deviation coefficient Z Rj is a function of the formation pressure P Rj , the formation pressure P at the j-th moment is obtained by iteration through formula (9) Rj .

[0037] The formation pressure P Rj needs to know the cumulative gas production ΔG from the end of the stable production period to the j-th moment pj . Through the integration of the production decline equation, the cumulative gas production ΔG from the end of the stable production period to the j-th moment pj is:

[0038]

[0039] The technical effect of the present invention lies in:

[0040] The present invention combines the gas well productivity equation, material balance equation, and decline formula of a constant-volume closed gas reservoir, and proposes a method for quickly predicting the decline rate of a production gas well. The decline rate of the gas well can be predicted during the stable production stage of the gas well, effectively solving the problem that the decline rate cannot be predicted during the stable production stage of the gas well; at the same time, since it is difficult to obtain parameters such as the effective permeability of the gas layer and the total skin factor in the gas well productivity equation, and the error is large, the present invention eliminates the influence of the parameters by using the ratio of gas production at different moments, greatly improving the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is the actual decline fitting diagram of Well S12 of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0042] A method for predicting the decline rate of a gas well in a constant-volume closed gas reservoir is as follows:

[0043] Step 1: Assume the initial value of the decline rate D(0), and obtain the annual gas production ΔG after decline in the first year according to the following formula p1 (0);

[0044]

[0045] Step 2: Assume the initial formation pressure P R1 0 (0) at the end of the first year after the decline of the gas well, and require P R1 0 (0) < P Ri , and obtain the corresponding initial deviation factor Z R1 0 (0), and calculate the formation pressure P R1 1 (0) of the gas well after one year of decline;

[0046]

[0047] Judge |P R1 0 (0) - P R1 1 (0)| / P R1 1 (0) < 0.5%, then P R1 1 (0) is the formation pressure P R1 (0) at the end of the first year after the decline of the gas well; if |P R1 0 (0) - P R1 1 (0) / P R1 1 (0) ≥ 0.5%, then use P R1 1 (0) as the starting value to iterate step 2 until |P R1 m-1 (0) - P R1 m (0) / P R1 m (0) < 0.5%, and take P R1 m (0) as the formation pressure P R1 (0) at the end of the first year after the decline of the gas well;

[0048] Step 3: Calculate the daily gas production q 1 (0) at the end of the first year after the decline;

[0049]

[0050] Step 4: Calculate the gas well decline rate D’(0)

[0051]

[0052] Step 5: Error judgment: If |D’(0)-D(0)| / D’(0) < 1%, then D’(0) is the decline rate D of the gas well;

[0053] If |D’(0)-D(0)| / D’(0) ≥ 1, then use D’(0) as the initial value D(1) of the decline rate, and repeat Steps 1 - 5.

[0054] The loop content is as follows:

[0055] Step 1: D(1) = D’(0), and calculate the gas production ΔG in the first year after decline according to the following formula p1 (1);

[0056]

[0057] Step 2: P R1 0 (1) = P R1 (0), and obtain the initial value Z of the corresponding deviation coefficient R1 0 (1), and calculate the formation pressure P of the gas well after one year of decline R1 1 (1);

[0058]

[0059] Judge |P R1 0 (1)-P R1 1 (1) / P R1 1 (1) < 0.5%, then P R1 1 (1) is the formation pressure P at the end of the first year after the decline of the gas well R1 (0); If |P R1 0 (1)-P R1 1 (1) / P R1 1 (1) ≥ 0.5%, then use P R1 1 (1) as the starting value to start the iteration of Step 2 until |P R1 m-1 (0)-P R1 m (0) / P R1 m (0) < 0.5%, and use P R1 m (1) as the formation pressure P at the end of the first year after the decline of the gas well R1 (1);

[0060] Step 3: Calculate the daily gas production q at the end of the first year after the decline 1 (1);

[0061]

[0062] Step 4: Calculate the gas well decline rate D’(1)

[0063]

[0064] Step 5: Error judgment: If |D’(1) - D(1)| / D’(1) < 1%, then D’(1) is the gas well decline rate D. If not satisfied, repeat the loop until |D’(n) - D(n)| / D’(n) - < 1%, then D’(n) is the gas well decline rate D.

[0065] Specific experimental example

[0066] Taking S12 in the southeastern Ordos Basin as an example, the original formation pressure P of this well i is 20.763 MPa, the daily gas production q during the stable production period i is 24000 m 3 / d, the dynamic reserve G of the gas well is 0.92×10 8 m 3 , the lowest bottom hole flowing pressure P wfb is 5.5 MPa, the formation pressure P at the end of the stable production period Ri is 13.0401 MPa, and the deviation coefficient Z corresponding to the original formation pressure P is obtained by high-pressure physical property interpolation i is 0.9426, the deviation coefficient Z corresponding to P i is 0.9344, the natural gas viscosity μ corresponding to P Ri is 0.0165 mPa·s. Ri Ri gi -1 p1 (0);

[0067] A method for predicting the production decline rate of a gas well in a constant-volume closed gas reservoir is as follows:

[0068] A method for predicting the production decline rate of a gas well in a constant-volume closed gas reservoir is as follows:

[0069] 1. Assume the initial decline rate D(0) = 0.001 d -1 , calculate the cumulative gas production ΔG within one year after the decline p1 (0):

[0070]

[0071] 2. Assume the initial value of the formation pressure one year after the gas well decline The initial value of the corresponding deviation coefficient = 0.9386, calculate the formation pressure at the end of the first year after decline

[0072]

[0073] Error judgment: Conduct the first iteration; take as the initial value of the formation pressure after one year of decline, repeat step 2, and calculate to obtain Judge again Therefore, calculate the formation pressure P R1 (0) is 11.4354 MPa;

[0074] 3. P R1 (0) corresponds to a deviation factor of Z R1 (0) = 0.9437, μ R1 (0) = 0.0161 mPa·s, calculate the daily gas production q 1 (0):

[0075]

[0076] 4. Calculate the gas well decline rate D′(0):

[0077]

[0078] 5. Error judgment: |D′(0) - D(0)| / D′(0) = |0.000836 - 0.001| / 0.000836 = 19.62% > 1%; conduct the first iteration; take D′(0) as the initial value D(1) of the gas well decline rate, iterate steps 1 - 5, and calculate to obtain ΔG p1 (1) = 7549659.8 m 3 ;

[0079] P R1 (1) = 11.3882 MPa; q 1 (1) = 17626.93 m 3 , D′(1) = 0.000846 d -1 ;

[0080] Judge again |D′(1) - D(1)| / D′(1) = |0.000846 - 0.000836| / 0.000846 = 1.18% > 1%, conduct the second iteration;

[0081] Take D′(1) as the initial value D(2) of the gas well decline rate, iterate steps 1 - 5, and calculate to obtain ΔG p1 (2) = 7536596.8 m3 ;

[0082] P R1 (2) = 11.3924 MPa; q 1 (2) = 17436.16 m 3 , D′(2) = 0.000875d -1 ;

[0083] Judge again that |D′(2) - D(2)| / D′(2) = |0.000875 - 0.000846| / 0.000875 = 3.31% > 1%; perform the third iteration;

[0084] Take D′(2) as the initial value D(3) of the decline rate, and iterate steps 1 - 5 to calculate ΔG p1 (3) = 7498888.5 m 3 ;

[0085] P R1 (3) = 11.4008 MPa; q 1 (3) = 17452.94 m 3 , D′(3) = 0.000873d -1 ;

[0086] Judge again that |D′(3) - D(3)| / D′(3) = |0.000873 - 0.000875| / 0.000873 = 0.23% < 1%, so D′(3) is the final value of the gas well decline rate D, that is, 0.000873d -1 .

[0087] Actual decline fitting data, see Figure 1 , and the fitted gas well decline rate is 0.000837d -1 , and the result analysis shows that the error between the present invention and the actual data is 4.30%, meeting the accuracy requirements.

Claims

1. A method for predicting the production decline rate of gas wells in a constant-volume closed gas reservoir, characterized in that: the method is as follows: Step 1: Take D(n) with the initial value of the decline rate, and obtain the annual gas production △G in the first year after decline according to the following formula p1 (n); Where: ΔG p1 (n) is the annual gas production in the nth iteration of the first year after decline, m 3 ; q i is the daily gas production during the stable production period, m 3 / d; D(n) is the initial value of the decreasing rate for the nth iteration, d -1 ; n is the number of iterations of the decreasing rate, n = 0, 1, 2, ……; Step 2: Obtain the initial formation pressure P R1 m-1 (n) at the end of the first year after the gas well decline, and require that P R1 m-1 (n) < P Ri , and obtain the corresponding initial deviation factor Z R1 m-1 (n), and calculate the formation pressure P R1 m (n) after one year of decline; Where: P R1 m-1 (n) is the initial formation pressure value at the end of the first year and the m-th iteration after the decline of the gas well, MPa; Z R1 m-1 (n) is P R1 m-1 (n) corresponds to the deviation coefficient, dimensionless; P R1 m (n) is the formation pressure value at the end of the first year after the decline of the gas well for the m-th iteration, MPa; P Ri is the formation pressure at the end of stable production, MPa; Z Ri is for P Ri corresponding deviation factor, dimensionless; P i is the original formation pressure, MPa; Z i corresponds to P i and the corresponding deviation factor, dimensionless; G is the dynamic reserve of the gas well, m 3 ; m is the number of formation pressure iterations, m = 1, 2, ……; If P R1 m (n) is the final formation pressure value P R1 (n) at the end of the first year after the decline of the gas well for the nth iteration; otherwise, use P R1 m (n) as the initial formation pressure value at the end of the first year after the decline of the gas well, and perform iteration until Step 3: Calculate the daily gas production q at the end of the first year after the decrease 1 (n); Where: q 1 (n) is the daily gas production at the end of the first year after decline, m 3 / d; μ gi is P Ri The corresponding natural gas viscosity, mPa·S; μ g1 (n) is P R1 (n) corresponding natural gas viscosity, mPa·S; Z Ri is P Ri The corresponding deviation coefficient, dimensionless; Z R1 (n) is P R1 (n) corresponds to the deviation coefficient, dimensionless; P wfb is the lowest bottom-hole flowing pressure, MPa; Step 4: Calculate the decline rate D′(n) of the gas well Where: D′(n) is the decline rate value of the gas well, d -1 ; If |D′(n) - D(n)| / D′(n) < 1%, then D′(n) is the decline rate D of the gas well; otherwise, take D′(n) as the initial value of the decline rate, and iterate steps 1 to 4 until |D′(n) - D(n)| / D′(n) < 1% is satisfied, then D′(n) is the decline rate D of the gas well; in step 2, take P R1 (n) as the initial value of the formation pressure at the end of the first year after the decline of the gas well.

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