Method for determining injection binomial productivity equation by gas storage stable point method

Abstract

A method for determining an injection binomial productivity equation through a gas storage stable point method belongs to the technical field of gas storage exploitation, starts from theoretical formula derivation, obtains the binomial productivity equation, ingeniously avoids interference of stratum coefficients on the binomial productivity equation, and improves the production efficiency. A new method mathematical model of the gas storage stable point method injection productivity equation is determined, and the problem that productivity well test interpretation cannot be carried out when the binomial slope decline is a negative value in productivity evaluation of a multi-point test well is solved; meanwhile, the problems that only one stable yield, stable flowing bottomhole pressure and formation pressure are measured, and binomial parameters of productivity well testing cannot be solved are solved, a basis is provided for calculating the injection capacity in the gas injection period, and the requirements for production and scientific research of a gas field and a mine field are met.

Description

Technical Field

[0001] The invention belongs to the technical field of gas storage exploitation, and in particular relates to a method for determining an injection binomial production capacity equation using a gas storage stability point method. Background Art

[0002] The primary function of underground gas storage is to regulate seasonal peaks and valleys in gas demand, or to ensure continuous gas supply in the event of an emergency. A gas storage operation consists of an injection period, a balance period, and a production period. Well test interpretation plays a crucial role in gas storage production. Well testing methods are crucial for determining injection capacity (the injection capacity equation), injection duration, formation parameters during the balance period, formation parameters during the production period, and production capacity during the production period. Typically, a gas storage well test involves inserting an electronic pressure gauge during the injection period and conducting injection tests using four operating modes. During the balance period, a pressure "drop" test is performed to determine the injection capacity (the injection capacity equation) and formation parameters during the injection period. However, when the downward slope of the binomial equation in the production capacity test is negative, the production capacity equation cannot be established. Under these circumstances, a new method for determining the injection capacity equation using the gas storage stability point method was developed, resulting in a new mathematical model for the injection capacity equation using the stability point method. Summary of the Invention

[0003] In order to solve the above-mentioned problems, the present invention proposes: a method for determining the injection binomial production capacity equation using the gas storage reservoir stability point method, starting from the theoretical formula deduction, deriving the binomial production capacity equation, avoiding the interference of the formation coefficient on the binomial production capacity equation, and determining the mathematical model of the method for determining the injection capacity equation using the gas storage reservoir stability point method.

[0004] Furthermore, for a gas zone with boundary restrictions, when the pressure change reaches the boundary, or when the formation pressure changes into a pseudo-steady state, the relationship between pressure and production is expressed as:

[0005]

[0006] Where:

[0007] S a =S+Dq g

[0008] S a --apparent skin coefficient;

[0009] S--true skin coefficient;

[0010] D--non-Darcy flow coefficient, (m 3 / d) -1 ;

[0011] q g--Stable gas injection volume; 10 4 m 3 / d;

[0012] p wf --Flow pressure, MPa;

[0013] p R --formation pressure, MPa;

[0014] --Average viscosity of gas under formation conditions, mPa·s;

[0015] --Gas deviation coefficient under formation conditions;

[0016] --Average gas temperature under formation conditions, °K

[0017] p sc --Gas pressure under standard conditions, 0.101MPa

[0018] K--effective permeability of the formation, mD;

[0019] h--effective thickness of the formation, m;

[0020] T sc --Gas temperature under standard conditions, 293.15°K;

[0021] r e --Detection radius, m;

[0022] r w --Well conversion radius, m;

[0023] First, simplify (Formula 1) into a binomial capacity equation as follows:

[0024] p wf 2 -p R 2 =Aq g +Bq g 2 (Formula 2)

[0025] Where A and B are two constants related to the gas layer characteristic parameters and natural gas physical parameters. They are coefficients describing Darcy flow and non-Darcy flow.

[0026] Furthermore, multiplying both sides of the binomial equation by the formation coefficient Kh yields:

[0027] Kh(p wf 2 -p R 2)=A(Kh)q g +B(Kh)q g 2 (Formula 3)

[0028] So,

[0029] So,

[0030] Furthermore,

[0031] Substituting Kh into (Formula 4) yields:

[0032]

[0033] Then, the binomial A value is,

[0034] Furthermore, substituting Kh into (Formula 5) yields:

[0035]

[0036] Then, the binomial B value is,

[0037] Furthermore, from (Formula 9), it can be concluded that the non-Darcy flow coefficient D is unknown, while other parameters are known. Through repeated testing and calculation of oil and gas fields, the non-Darcy flow coefficient D is determined to be 0.02-0.15×10 4 m 3 / d -1 between.

[0038] Furthermore, the formation pressure p of the test well is R , flow pressure p wf , formation temperature T and gas composition are calculated Then the skin coefficient S and detection radius r in the pressure recovery test interpretation results are e Substitute the parameter values ​​such as the non-Darcy flow coefficient D into (Formula 4) and (Formula 5) to calculate A(Kh) and B(Kh).

[0039] Furthermore, A(Kh), B(Kh), p R 、p wf ,q g Substitute into (Formula 6) to determine the formation coefficient Kh, in mD·m.

[0040] Furthermore, Kh is substituted into (Formula 8) and (Formula 9) to obtain the values ​​of A and B, thereby determining the parameters of the binomial equation of the well productivity equation.

[0041] Furthermore, the binomial capacity equation is: pwf 2 -p R 2 =A (数值) q g +B (数值) q g 2 and provide a basis for calculating the injection capacity during the gas injection period.

[0042] The beneficial effects of the present invention are as follows: the present invention discloses a new method model parameters for determining the injection productivity equation using the gas storage stability point method, and according to the geological characteristics of gas reservoirs of various gas storages, the new method model parameters for determining the injection productivity equation using the gas storage stability point method are re-optimized and determined based on detailed analysis and evaluation of sufficient gas storage injection well test data.

[0043] The present invention starts with deduction of theoretical formulas and derives a binomial productivity equation, cleverly avoiding the interference of formation coefficients on the binomial productivity equation, and determines a new method mathematical model for the injection productivity equation of the gas storage stable point method. This solves the problem of being unable to interpret productivity well tests when the binomial slope is negative in the productivity evaluation of multi-point test wells; at the same time, it also solves the problem of being unable to obtain the binomial parameters of the productivity well test when only a stable production and a stable bottom hole flow pressure and formation pressure are measured, providing a basis for calculating the injection capacity during the gas injection period, and meeting the production and scientific research requirements of the gas field mine. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of a new method for determining the injection capacity equation using the gas storage stability point method in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] To make the technical means and objectives of the present invention easier to understand, the present invention is further described below in conjunction with specific embodiments. A method for determining the injection binomial capacity equation using the gas storage stability point method can calculate the injection capacity during the injection period, reduce costs, and improve the utilization of existing data. The present application provides the injection capacity during the injection period, including:

[0046] For a gas zone with boundary restrictions, when the pressure change reaches the boundary, or when the formation pressure changes into a pseudo-steady state, the relationship between pressure and production is expressed as:

[0047]

[0048] Where:

[0049] S a =S+Dq g

[0050] S a --apparent skin coefficient;

[0051] S--true skin coefficient;

[0052] D--non-Darcy flow coefficient, (m 3 / d) -1 ;

[0053] q g --Stable gas injection volume; 10 4 m 3 / d;

[0054] p wf --Flow pressure, MPa;

[0055] p R --formation pressure, MPa;

[0056] --Average viscosity of gas under formation conditions, mPa·s;

[0057] --Gas deviation coefficient under formation conditions;

[0058] --Average gas temperature under formation conditions, °K

[0059] p sc --Gas pressure under standard conditions, 0.101MPa

[0060] K--effective permeability of the formation, mD;

[0061] h--effective thickness of the formation, m;

[0062] T sc --Gas temperature under standard conditions, 293.15°K;

[0063] r e --Detection radius, m;

[0064] r w --Well conversion radius, m;

[0065] First, simplify (Formula 1) into a binomial capacity equation as follows:

[0066] p wf 2 -p R 2 =Aq g +Bq g 2 (Formula 2)

[0067] Where A and B are two constants related to the gas layer characteristic parameters and natural gas physical parameters. They are coefficients describing Darcy flow and non-Darcy flow.

[0068] Multiply both sides of the binomial equation by Kh to get:

[0069] Kh(p wf 2 -p R 2 )=A(Kh)q g +B(Kh)q g 2 (Formula 3)

[0070] So,

[0071] So,

[0072] It can be deduced from (Formula 3) that

[0073] Substituting Kh into (Formula 4) yields:

[0074]

[0075] Substituting Kh into (Formula 5) yields:

[0076]

[0077] Then, the binomial A value is,

[0078] Then, the binomial B value is,

[0079] As can be seen from the formula (Formula 8), the non-Darcy flow coefficient D is unknown, while the other parameters are known. Therefore, it is particularly important to determine the D value. In the design of gas field development plans, the D value is the turbulence formed near the bottom of the well, which is the main component of the pseudo-skin. The causes of turbulence are complex and difficult to estimate using theoretical methods. It can only be obtained through testing. Through repeated testing and calculations of the Jilin Oil and Gas Field, the non-Darcy flow coefficient D value was determined to be 0.02~0.15×10 4 m 3 / d -1 Of.

[0080] The formation pressure p of the test well R , flow pressure p wf , formation temperature and gas composition Then the skin coefficient S and detection radius r in the pressure recovery test interpretation results are e Substitute the parameter values ​​such as the non-Darcy flow coefficient D into formula (Formula 4) and (Formula 5) to calculate A(Kh) and B(Kh).

[0081] A(Kh), B(Kh), p R 、p wf ,q g Substitute into (Formula 6) to determine Kh.

[0082] Substituting Kh into formulas (Formula 7) and (Formula 8), the values ​​of A and B are obtained, thereby determining the parameters of the binomial equation of the well's productivity equation.

[0083] The binomial capacity equation is: p wf 2 -p R 2 =A (数值) q g +B (数值) q g 2 and provide a basis for calculating the injection capacity during the gas injection period.

[0084] For well test data without equilibrium period pressure drop, the skin coefficient can be input as 0 and the detection radius is 220m.

[0085] The present invention provides a new method for determining the injection capacity equation using the gas storage stability point method, which can calculate the injection capacity during the injection period, reduce costs, and improve the utilization of existing data. The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.

[0086] like Figure 1 As shown, the present application implements the method of providing the injection capacity size during the gas injection period, and the method includes:

[0087] Step 301: The formation temperature p of well 1 and well 1 is R =12MPa, p wf =12.69MPa,q g =7.7676×10 4 m 3 / d and gas composition Then the skin coefficient S=12.57 and the detection radius r in the pressure recovery test interpretation results are e =315m and non-Darcy flow coefficient D = 0.12×10 4 m 3 / d -1 Enter the value into the system.

[0088] Step 302: Provide an expression for the relationship between pressure and production for a gas zone with boundary restrictions, after the pressure change reaches the boundary, or after the formation pressure change enters a pseudo-steady state.

[0089] Step 303: The expression of the relationship between pressure and output is simplified to a binomial production capacity equation.

[0090] Step 304: Multiply both sides of the simplified binomial production capacity equation by Kh to obtain a new equation.

[0091] Step 101: Substitute various parameters into the formula (Formula 4) to obtain A(Kh)=1033.16.

[0092] Step 201: Substitute various parameters into the formula (Formula 5) to obtain B(Kh)=6.13.

[0093] Step 305: Substitute step 101: A(Kh) and step 201: B(Kh) into (Formula 6) to obtain the formation coefficient Kh = 495.57 mD·m.

[0094] Step 102: Substitute the formation coefficient Kh=495.57mD·m into (Formula 7) to obtain the binomial parameter A, A=2.0848.

[0095] Step 202: Substitute the formation coefficient Kh=495.57mD·m into (Formula 8) to obtain the binomial parameter B, B=0.0123627.

[0096] Step 306: The parameters of the binomial productivity equation of the well are determined. The binomial productivity equation is: p wf 2 -p R 2 =2.0848q g +0.0123627q g 2 , output and preservation of results.

[0097] The new method flow chart for determining the injection productivity equation using the gas storage stability point method was strictly followed and 12 well-times were calculated for 4 wells. The average relative error of the A value was 0.92%, and the average relative error of the B value was 2.58%.

[0098] Comparison table of A and B values ​​of the injection binomial production capacity equation calculated by the gas storage stability point method

[0099]

[0100] The present invention applies binomial model parameters to gas storage well productivity testing during the injection phase. This derivation of the binomial productivity equation from a theoretical formula cleverly avoids interference from formation coefficients on the binomial productivity equation. Because the parameters in this formula are derived from actual values ​​in the Jilin gas field and verified at the mine site, they are suitable for evaluating gas storage well productivity during the injection phase and meet the production and scientific research requirements of the gas field. This solves the problem of being unable to interpret productivity testing when the binomial slope is negative in the productivity evaluation of multi-point test wells. It also addresses the difficulty of determining the binomial parameters for productivity testing when only a stable production rate, stable bottomhole pressure, and formation pressure are measured. This provides a basis for calculating injection capacity during the injection phase. The calculated relative error of the binomial A value is 0.92%, and the calculated relative error of the binomial B value is 2.58%, both of which are suitable for widespread application. Thus, the present invention achieves a higher accuracy in determining the injection binomial productivity equation using the gas storage stable point method.

[0101] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed in the present invention, who makes equivalent replacements or changes based on the technical solutions and concepts of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for determining the injection binomial production capacity equation using the gas storage stability point method, characterized in that: Starting from the theoretical formula, the binomial production capacity equation is derived, the interference of the formation coefficient on the binomial production capacity equation is avoided, and the mathematical model of the gas storage stable point method injection production capacity equation is determined.

2. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 1, characterized in that: For a gas zone with boundary restrictions, when the pressure change reaches the boundary, or when the formation pressure changes into a pseudo-steady state, the relationship between pressure and production is expressed as: Where: S a =S+Dq g S a --apparent skin coefficient; S--true skin coefficient; D--non-Darcy flow coefficient, (m 3 / d) -1 ; q g --Stable gas injection volume; 10 4 m 3 / d; p wf --Flow pressure, MPa; p R --formation pressure, MPa; --Average viscosity of gas under formation conditions, mPa·s; --Gas deviation coefficient under formation conditions; --Average gas temperature under formation conditions, °K p sc --Gas pressure under standard conditions, 0.101MPa K--effective permeability of the formation, mD; h--effective thickness of the formation, m; T sc --Gas temperature under standard conditions, 293.15°K; r e --Detection radius, m; r w --Well conversion radius, m; First, simplify (Formula 1) into a binomial capacity equation as follows: p wf 2 -p R 2 =Aq g +Bq g 2 (Formula 2) Where A and B are two constants related to the gas layer characteristic parameters and natural gas physical parameters. They are coefficients describing Darcy flow and non-Darcy flow.

3. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 2, characterized in that: Multiply both sides of the binomial equation by the formation coefficient Kh to obtain: Kh(p wf 2 -p R 2 )=A(Kh)q g +B(Kh)q g 2 (Formula 3) So, So, 4. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 3, wherein: Substituting Kh into (Formula 4) yields: Then, the binomial A value is, 5. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 4, characterized in that: Substituting Kh into (Formula 5) yields: Then, the binomial B value is, 6. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 5, characterized in that: From (Formula 9), it can be concluded that the non-Darcy flow coefficient D is unknown, while other parameters are known. Through repeated testing and calculation of oil and gas fields, the non-Darcy flow coefficient D is determined to be 0.02 to 0.15×10 4 m 3 / d -1 between.

7. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 6, characterized in that: The formation pressure p of the test well R , flow pressure p wf , formation temperature and gas composition Then the skin coefficient S and detection radius r in the pressure recovery test interpretation results are e Substitute the parameter values ​​such as the non-Darcy flow coefficient D into (Formula 4) and (Formula 5) to calculate A(Kh) and B(Kh).

8. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 7, characterized in that: A(Kh), B(Kh), p R 、p wf ,q g Substitute into (Formula 6) to determine the formation coefficient Kh, in mD·m.

9. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 7, wherein: Substitute Kh into (Formula 8) and (Formula 9) to calculate the values ​​of A and B, thereby determining the parameters of the binomial equation of the well's productivity equation.

10. The method for determining the injection binomial production capacity equation using the gas storage stability point method according to claim 9, characterized in that: The binomial capacity equation is: p wf 2 -p R 2 =A (数值) q g +B (数值) q g 2 and provide a basis for calculating the injection capacity during the gas injection period.

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