A method for calculating the degree of interference between tight gas wells

Abstract

The present invention relates to the technical field of oil and gas field development, and specifically to a method for calculating the degree of interference between tight gas wells. The method is as follows: for two tight gas wells located in the same production layer, the control radius of the two tight gas wells and the well spacing between the two tight gas wells are respectively obtained, and the well spacing between the two tight gas wells is substituted into a formula to calculate the degree of interference between the two tight gas wells. When the degree of interference between the two tight gas wells is equal to 0, it indicates that there is no interference between the two tight gas wells; when the degree of interference between the two tight gas wells is greater than 0, it indicates that there is interference between the two tight gas wells. The present invention establishes a method for calculating the degree of interference between tight gas wells based on the production capacity equation, the seepage equation, the material balance equation and the well spacing, which is of great significance for evaluating the residual gas distribution and the well network optimization.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development, and in particular to a method for calculating the degree of interference between tight gas wells. Background Art

[0002] When two oil and gas wells not far from each other in the same production layer produce at the same time, they will have different degrees of well interference due to the influence of reservoir physical properties, fluid characteristics and working system. Well interference phenomenon is common in the development of oil and gas reservoirs. Evaluating the degree of well interference is the basis for adjusting the working system and optimizing the well network. The research on well interference is currently mainly focused on coalbed methane wells, shale gas wells and oil wells. The research methods mainly include interference well test method, physical simulation, numerical simulation, moving window method, interference probability calculation and other methods. The use conditions and applicability of different methods vary greatly.

[0003] There are many wells for the development of tight gas reservoirs, and the single well production is low. Well density is the main means to improve the recovery rate of tight gas reservoirs. Rapid assessment of the degree of interference between wells is more important for tight gas wells. Since the development mechanism of tight gas wells is different from that of the above-mentioned gas wells, the current method cannot be directly applied. The flow of tight gas in the production layer follows the basic principles of gas reservoir engineering, seepage mechanics and material balance. Through the study of basic principles, a method for calculating the degree of interference between wells in tight gas wells is established, which has practical significance for the efficient development of tight gas. Summary of the invention

[0004] The present invention aims to solve the above problems and proposes a method for calculating the degree of interference between tight gas wells.

[0005] The technical solution of the present invention is.

[0006] A method for calculating the degree of interference between tight gas wells, the principle is as follows:

[0007] According to the principles of gas reservoir engineering, the production capacity equation of a fixed-yield tight gas well can be expressed as:

[0008]

[0009] Where: is the pseudo-average formation pressure, MPa 2 / mPa·s; ψ(p wf ) is the pseudo bottom hole pressure, MPa 2 / mPa·s;

[0010] q sc is the gas production of tight gas wells under standard conditions, m 3 / d;

[0011] K is the gas reservoir permeability, 10 -3 μm 2; h is the thickness of the gas reservoir, m;

[0012] T is the gas reservoir temperature, K; T sc is standard temperature, K;

[0013] p sc is the standard pressure, MPa; r e is the control radius, m; r w is the well bottom radius, m.

[0014] According to the principle of seepage mechanics, the seepage equation of a fixed-yield tight gas well can be expressed as:

[0015]

[0016] Where: ψ(p i ) is the pseudo original formation pressure, MPa 2 / mPa·s;

[0017] is the porosity, dimensionless;

[0018] t is time, d;

[0019] μ is the gas viscosity, mPa·s;

[0020] C g is the isothermal compressibility, MPa -1 .

[0021] By combining the capacity equation and the seepage equation, we can derive:

[0022]

[0023] Where: G p is the cumulative gas production, m 3 / d;

[0024] In formula (3), μ and C g yes The function of are μ, Z and In order to reduce the complexity of the calculation process and improve the calculation efficiency, the high-pressure physical property parameters in the original state are used to derive the calculation formula for the control radius of tight gas wells:

[0025]

[0026] Where: (μC g ) i μC in its original state g , mPa·s / MPa; (μZ) i is μZ in the original state, mPa·s;

[0027] p i is the original formation pressure, MPa; is the average formation pressure, MPa.

[0028] According to the material balance principle, the material balance equation of constant volume gas drive tight gas wells can be expressed as:

[0029]

[0030] Where: Z r for The corresponding deviation coefficient is dimensionless; Z i is the original deviation coefficient, dimensionless;

[0031] S gi is the original gas saturation, dimensionless;

[0032] Both formula (4) and formula (5) contain two variables: control radius r e and average formation pressure The tight gas well control radius r is solved by iteration. e .

[0033] For any two tight gas wells α and β located in the same production layer, their well spacing can be calculated using the wellhead coordinates:

[0034]

[0035] Where: L αβ is the well distance between tight gas well α and tight gas well β, m;

[0036] (x α ,y α ) is the wellhead coordinate of tight gas well α; (x β ,y β ) is the wellhead coordinate of tight gas well β.

[0037] For any two tight gas wells α and β located in the same production layer, when the sum of the control radii r eα +r eβ Greater than well spacing L αβ When the sum of the control radii r eα +r eβ Less than or equal to well spacing L αβ , it indicates that there is no inter-well interference between tight gas well α and tight gas well β.

[0038] Based on the above principle, the sgn(x) function is introduced to establish the calculation formula for the degree of interference between tight gas wells:

[0039]

[0040] Where: αβ is the degree of inter-well interference between tight gas well α and tight gas well β, dimensionless;

[0041] r eα is the control radius of any tight gas well α, m; r eβ is the control radius of any tight gas well β, m;

[0042] sgn(x) is a mathematical function. When x<0, sgn(x)=-1; when x=0, sgn(x)=0; when x>0, sgn(x)=1.

[0043] Since the sgn(x) function is used, the well interference degree ω αβ The value range of ≥0:

[0044] (1) When ω αβ = 0, indicating that there is no inter-well interference between tight gas well α and tight gas well β;

[0045] (2) When ω αβ When >0, it indicates that there is inter-well interference between tight gas well α and tight gas well β.

[0046] The technical effects of the present invention are:

[0047] The present invention establishes a method for calculating the degree of interference between tight gas wells based on the production capacity equation, seepage equation, material balance equation and well spacing, which is of great significance for evaluating the distribution of residual gas and optimizing the well pattern. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is a schematic diagram of the final value of the control radius iteration and the iterative relative error of the present invention. DETAILED DESCRIPTION

[0049] Example 1

[0050] A method for calculating the degree of interference between tight gas wells is as follows:

[0051] For two tight gas wells located in the same production layer, the control radius of the two tight gas wells and the well spacing of the two tight gas wells are obtained respectively, and the inter-well interference degree between the two tight gas wells is calculated by substituting them into the following formula:

[0052]

[0053] Where: αβ is the degree of inter-well interference between tight gas well α and tight gas well β, dimensionless;

[0054] r eαis the control radius of any tight gas well α, m;

[0055] r eβ is the control radius of any tight gas well β, m;

[0056] L αβ is the well distance between tight gas well α and tight gas well β, m;

[0057] sgn(x) is a mathematical function. When x is less than 0, sgn(x) = -1; when x is equal to 0, sgn(x) = 0; when x is greater than 0, sgn(x) = 1.

[0058] Determine the degree of inter-well interference ω between tight gas well α and tight gas well β αβ

[0059] (1) When ω αβ = 0, indicating that there is no inter-well interference between tight gas well α and tight gas well β;

[0060] (2) When ω αβ When >0, it indicates that there is inter-well interference between tight gas well α and tight gas well β.

[0061] Example 2

[0062] Based on Example 1, the calculation process of the control radius is:

[0063] (1) Assume that the initial value of the control radius is r e (0) is [10,1000];

[0064] (2) Determine the initial value r of the control radius iteration e begin (k)

[0065] When k = 0, the initial value of the control radius iteration r e begin (k) = initial control radius r e (0);

[0066] When k>0, the initial value of the control radius iteration for the kth time r e begin (k) = final value of the control radius iteration of the k-1th time r e end (k-1);

[0067] (3) Calculation of average formation pressure

[0068]

[0069] Where: is the average formation pressure, MPa; r eis the control radius, m;

[0070] Z r for The corresponding deviation coefficient is dimensionless; Z i is the original deviation coefficient, dimensionless;

[0071] p i is the original formation pressure, MPa; p sc is standard pressure, MPa;

[0072] T is the gas reservoir temperature, K; T sc is standard temperature, K;

[0073] G p is the cumulative gas production, m 3 / d;

[0074] h is the thickness of the gas reservoir, m; is the porosity, dimensionless; S gi is the original gas saturation, dimensionless;

[0075] (4) Calculate the final value r of the control radius iteration e end (k)

[0076]

[0077] Where: (μC g ) i μC in its original state g ,mPa·s / MPa;(μZ) i is μZ in the original state, mPa·s;

[0078] (5) Determine the final value r of the control radius iteration e end (k) Is it effective?

[0079] If the iterative relative error between the final value of the control radius iteration and the initial value of the control radius iteration |r e end (k)-r e begin (k)| / r e end (k)≤1%, then the final value of the kth control radius iteration r e end (k) is valid, let the control radius r e = final value of control radius iteration r for the kth time e end (k);

[0080] If the iterative relative error between the final value of the control radius iteration and the initial value of the control radius iteration |re end (k)-r e begin (k)| / r e end (k)>1%, then the final value of the kth control radius iteration r e end (k) is invalid, and the final value of the control radius iteration of the kth time is r e end (k) = initial value r of the control radius iteration for the k+1th time e begin (k+1), repeat steps (2) to (5) to continue iterating until the final value of the control radius iteration is valid.

[0081] Example 3

[0082] Based on Example 2, the calculation process of the well spacing is:

[0083]

[0084] Where: L αβ is the well distance between tight gas well α and tight gas well β, m;

[0085] (x α ,y α ) is the wellhead coordinate of tight gas well α;

[0086] (x β ,y β ) is the wellhead coordinate of tight gas well β.

[0087] Specific experimental examples

[0088] Well 1, Well 2 and Well 3 are tight gas wells, and their production layer is all in Shan 2. The degree of interference between Well 1, Well 2 and Well 3 is calculated respectively. For the convenience of comparison, the cumulative gas production G on January 1, 2015 is selected. p As calculation data, detailed calculation parameters are shown in Table 1.

[0089] Table 1 Calculation parameters

[0090]

[0091] Step 1: Calculate the control radius r e .

[0092] (1) Assume that the initial value of the control radius is r e (0) is [10,1000];

[0093] Assume that the initial values ​​of the control radius of well 1, well 2 and well 3 are: r e1 (0) = 100; re2 (0) = 100; r e3 (0)=100.

[0094] (2) Determine the initial value r of the control radius iteration e begin (k)

[0095] When the number of iterations of well 1 is k 1 = 0, the number of iterations k of well 2 2 = 0, number of iterations k of well 3 3 = 0,

[0096] The initial values ​​of the control radius iteration are:

[0097] The initial value r of the control radius iteration of well 1 e1 begin (k 1 =0) = r e1 (0) = 100;

[0098] The initial value r of the control radius iteration of well 2 e2 begin (k 2 =0) = r e2 (0) = 100;

[0099] The initial value r of the control radius iteration of well 3 e3 begin (k 3 =0) = r e3 (0)=100.

[0100] (3) Calculation of average formation pressure

[0101] Average formation pressure of Well 1

[0102] Average formation pressure of Well 2

[0103] Average formation pressure of Well 3

[0104] (4) Calculate the final value r of the control radius iteration e end (k)

[0105] The final value of the iteration of the control radius of well 1 is r e1 end (k 1 =0)=114.57m;

[0106] The final value of the iteration of the control radius of well 2 is r e2 end (k 2=0)=110.75m;

[0107] The final value of the control radius iteration r of well 3 e3 end (k 3 =0)=104.61m.

[0108] (5) Determine whether the final value of the control radius iteration is valid

[0109] Iterative relative error of well 1 |r e1 end (k 1 =0)-r e1 begin (k 1 =0)| / r e1 end (k 1 =0) = 12.72% > 1%, control radius iteration final value r e1 end (k 1 =0) is invalid, and the final value of the control radius iteration is r e1 end (k 1 =0) = initial value of control radius iteration r e1 begin (k 1 =1), repeat the steps

[0110] (2) Continue iterating to step (5);

[0111] Iterative relative error of well 2 |r e2 end (k 2 =0)-r e2 begin (k 2 =0)| / r e2 end (k 2 =0) = 9.71% > 1%, control radius iteration final value r e2 end (k 2 =0) is invalid, and the final value of the control radius iteration is r e2 end (k 2 =0) = initial value of control radius iteration r e2 begin (k 2 =1), repeat steps (2) to (5) to continue iterating;

[0112] Iterative relative error of well 3 |r e3 end (k 3 =0)-r e3begin (k 3 =0)| / r e3 end (k 3 =0) = 4.41% > 1%, control radius iteration final value r e3 end (k 3 =0) is invalid, and the final value of the control radius iteration is r e3 end (k 3 =0) = initial value of control radius iteration r e3 begin (k 3 =1), repeat steps (2) to (5) to continue iterating.

[0113] When the number of iterations of well 1 is k 1 =1, number of iterations k of well 2 2 =1, number of iterations k of well 3 3 =1,

[0114] The initial value r of the control radius iteration of well 1 e1 begin (k 1 =1) = 114.57m, final value of control radius iteration r e1 end (k 1 =1) = 130.85m, iterative relative error | r e1 end (k 1 =1)-r e1 begin (k 1 =1)| / r e1 end (k 1 =1)=12.44%>1%, control radius iteration final value r e1 end (k 1 =1) is invalid, repeat steps (2) to (5) to continue iterating.

[0115] The initial value r of the control radius iteration of well 2 e2 begin (k 2 =1)=110.75m, final value of control radius iteration r e2 end (k 2 =1) = 122.52m, iterative relative error | r e2 end (k 2 =1)-r e2 begin (k 2=1)| / r e2 end (k 2 =1) = 9.60% > 1%, control radius iteration final value r e2 end (k 2 =1) is invalid, repeat steps (2) to (5) to continue iterating.

[0116] The initial value r of the control radius iteration of well 3 e3 begin (k 3 =1)=104.61m, final value of control radius iteration r e3 end (k 3 =1) = 109.22m, iterative relative error | r e3 end (k 3 =1)-r e3 begin (k 3 =1)| / r e3 end (k 3 =1) = 4.22% > 1%, control radius iteration final value r e3 end (k 3 =1) is invalid, repeat steps (2) to (5) to continue iterating.

[0117] Increase the value of the number of iterations k and continue iterating. For the detailed iterative process, see Figure 1 , and finally get:

[0118] When k 1 =18, the initial value of the control radius iteration of well 1 is r e1 begin (k 1 =18)=387.98m, final value of control radius iteration r e1 end (k 1 =18)=391.61m, iterative relative error |r e1 end (k 1 =18)-r e1 begin (k 1 =18)| / r e1 end (k 1 =18) = 0.93% ≤ 1%, control radius iteration final value r e1 end (k 1 =18) is valid, and the control radius r of well 1 is obtained e1 =re1 end (k 1 =18)=391.61m.

[0119] When k 2 = 25, the initial value of the control radius iteration of well 2 is r e2 begin (k 2 =25)=461.10m, final value of control radius iteration r e2 end (k 2 =25) = 465.43m, iterative relative error | r e2 end (k 2 =25)-r e2 begin (k 2 =25)| / r e2 end (k 2 =25)=0.93%≤1%, control radius iteration final value r e2 end (k 2 = 25) is valid, and the control radius r of well 2 is obtained. e2 =r e2 end (k 2 =25)=465.43m.

[0120] When k 3 =19, the initial value of the control radius iteration of well 3 is r e3 begin (k 3 =19)=166.35m, final value of control radius iteration r e3 end (k 3 =19)=167.98m, iterative relative error |r e3 end (k 3 =19)-r e3 begin (k 3 =19)| / r e3 end (k 3 =19) = 0.97% ≤ 1%, control radius iteration final value r e3 end (k 3 =19) is valid, and the control radius r of well 3 is obtained e3 =r e3 end (k 3 =19)=167.98m.

[0121] Step 2: Calculate the well spacing L αβ

[0122] By formula (6), we can calculate

[0123] The distance between well 1 and well 2 is L 12 =776.66m;

[0124] The distance L between well 1 and well 3 13 =789.53m;

[0125] The distance L between well 2 and well 3 23 =833.14m.

[0126] Step 3: Calculate the degree of well interference

[0127] The degree of inter-well interference between different tight gas wells in the same production layer is calculated by formula (7): αβ :

[0128] Inter-well interference degree between well 1 and well 2 ω 12 =[1-sgn(1-sgn(80.37))]×10.35%=10.35%, indicating that there is inter-well interference between well 1 and well 2;

[0129] Inter-well interference degree between well 1 and well 3 ω 13 =[1-sgn(1-sgn(-229.95))]×(-29.12%)=0, indicating that there is no inter-well interference between well 1 and well 3;

[0130] Inter-well interference degree between well 2 and well 3 ω 23 =[1-sgn(1-sgn(-199.74))]×(-23.97%)=0, indicating that there is no inter-well interference between well 2 and well 3.

Claims

1. A method for calculating the degree of interference between tight gas wells, characterized by: Here’s how: For two tight gas wells located in the same production layer, the control radius of the two tight gas wells and the well spacing of the two tight gas wells are obtained respectively, and the inter-well interference degree between the two tight gas wells is calculated by substituting them into the following formula: Where: αβ is the degree of inter-well interference between tight gas well α and tight gas well β, dimensionless; r eα is the control radius of any tight gas well α, m; r eβ is the control radius of any tight gas well β, m; L αβ is the well distance between tight gas well α and tight gas well β, m; sgn(x) is a mathematical function, when x<0, sgn(x)=-1; When x=0, sgn(x)=0; when x>0, sgn(x)=1; Determine the degree of inter-well interference ω between tight gas well α and tight gas well β αβ (1) When ω αβ = 0, indicating that there is no inter-well interference between tight gas well α and tight gas well β; (2) When ω αβ When > 0, it indicates that there is inter-well interference between tight gas well α and tight gas well β; The calculation process of the control radius is: (1) Assume that the initial value of the control radius is r e (0) is [10,1000]; (2) Determine the initial value r of the control radius iteration e begin (k) When k = 0, the initial value of the control radius iteration r e begin (k) = initial control radius r e (0); When k>0, the initial value of the control radius iteration for the kth time r e begin (k) = final value of the control radius iteration of the k-1th time r e end (k-1); (3) Calculation of average formation pressure Where: is the average formation pressure, MPa; r e is the control radius, m; Z r For The corresponding coefficient of deviation is dimensionless; Z i is the original deviation coefficient, dimensionless; p i is the original formation pressure, MPa; p sc is standard pressure, MPa; T is the gas reservoir temperature, K; T sc is standard temperature, K; G p is the cumulative gas production, m 3 / d; h is the thickness of the gas reservoir, m; is the porosity, dimensionless; S gi is the original gas saturation, dimensionless; (4) Calculate the final value r of the control radius iteration e end (k) Where: (μC g ) i μC in its original state g ,mPa·s / MPa;(μZ) i is μZ in the original state, mPa·s; (5) Determine the final value r of the control radius iteration e end (k) Is it effective? If the iterative relative error between the final value of the control radius iteration and the initial value of the control radius iteration |r e end (k)-r e begin (k)| / r e end (k)≤1%, then the final value of the kth control radius iteration r e end (k) is valid, let the control radius r e = final value of control radius iteration r for the kth time e end (k); If the iterative relative error between the final value of the control radius iteration and the initial value of the control radius iteration |r e end (k)-r e begin (k)| / r e end (k)>1%, then the final value of the kth control radius iteration r e end (k) is invalid, and the final value of the control radius iteration of the kth time is r e end (k) = initial value r of the control radius iteration for the k+1th time e begin (k+1), repeat steps (2) to (5) to continue iterating until the final value of the control radius iteration is valid; The calculation process of the well spacing is: Where: L αβ is the well distance between tight gas well α and tight gas well β, m; (x α ,y α ) is the wellhead coordinate of tight gas well α; (x β ,y β ) is the wellhead coordinate of tight gas well β.

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