Calculation method of stratified gas leakage radius in combined production gas reservoirs

Abstract

The present invention relates to the technical field of oilfield development, and specifically to a method for calculating the stratified gas leakage radius of a combined production gas reservoir. A method for calculating the stratified gas leakage radius of a combined production gas reservoir, obtains the basic parameters of each production layer in the target well area, and then obtains the original formation pressure, current formation pressure and original formation temperature corresponding to the vertical depth of the middle of each production layer; constructs the relationship between the cumulative production of the metering gas well and the gas leakage radius of each production layer; establishes the relationship between the gas leakage radius of each production layer and the relationship between the natural gas deviation coefficient and the pressure, substitutes the relationship between the cumulative production of the metering gas well and the gas leakage radius of each production layer into the relationship equation about the gas leakage radius of each production layer, and then solves the gas leakage radius of each production layer. The method of the present invention is simple.

Description

Technical Field

[0001] The invention relates to the technical field of oilfield development, and in particular to a method for calculating the stratified gas leakage radius of a combined production gas reservoir. Background Art

[0002] Conventional methods for calculating the gas leakage radius include the test method and the calculation method. Both methods first split the cumulative gas production of the gas well into each production layer, then set a regular gas supply shape (mostly set to a circle), and calculate the gas leakage radius based on the physical properties and gas content parameters of each production layer. The test method is more accurate, but the cost of gas production profile testing is high, the operation is complicated when splitting the production, and it is greatly affected by the test results, test frequency, etc. Other types of production splitting calculation methods are based on reservoir parameters, such as the KH method, or use mathematical algorithms, such as the mutation theory coefficient method. These methods are based on the physical properties of the production layer. The calculation results are affected by the method and the parameters used, and the errors are large. Summary of the invention

[0003] The present invention is based on the material balance principle and adopts the gas state equation to establish the relationship between the measured cumulative gas production and the gas leakage radius of each production layer, so as to calculate the gas leakage radius of each production layer in real time according to the measured cumulative gas production, parameters of each production layer and other data.

[0004] The technical solution of the present invention is: According to the material balance principle and the gas state equation, the natural gas produced from the dry gas reservoir during the production process satisfies the following equation under the standard surface conditions and the original formation pressure conditions: Where: Z i is the natural gas deviation coefficient under original formation conditions, decimal; p i H pi Original formation pressure corresponding to vertical depth, MPa; H pi is the vertical depth of the original formation pressure measurement point, m; V i is the gas volume under original formation conditions, m 3 ; T i is the gas temperature under original formation conditions, K; Z sc is the natural gas deviation coefficient under ground standard conditions, decimal; p sc is the pressure under standard ground conditions, MPa; V sc is the volume of gas under standard ground conditions, m 3 ; T sc is the gas temperature under standard ground conditions, K.

[0005] During the production of a gas well, the formation pressure corresponding to the vertical depth of a certain measuring point in the wellbore can be obtained at a certain moment by testing or calculation. When the production of the gas well is stable, the wellbore is a connected system, the gas flow rate is low, and the friction resistance can be ignored during the calculation process. According to the principle of the connecting vessel, the pressure coefficient method is used to obtain the formation pressure corresponding to the vertical depth of the measuring point; (1) The specific solution process of the current formation pressure corresponding to the vertical depth in the middle of each production layer is: p j = p / H p ·H j (2-1) Where p j is the current formation pressure corresponding to the vertical depth of the middle of the j-producing layer, MPa; H p is the vertical depth of the current formation pressure measurement point, m; p is H p Current formation pressure corresponding to vertical depth, MPa; H j is the vertical depth corresponding to the middle of the j-producing layer, m; (2) The specific solution process of the original formation pressure corresponding to the vertical depth of the middle part of each production layer is as follows: p ij = p i / H pi ·H j (2-2) Where: p ij is the original formation pressure corresponding to the vertical depth of the middle part of the j-producing layer, MPa; H pi is the vertical depth of the original formation pressure measurement point, m; p i H pi The original formation pressure corresponding to the vertical depth, MPa.

[0006] Generally, the temperature change in the wellbore satisfies the following relationship: T ij = T0+(H j -H0)D T (3) Where: T ij is the original formation temperature corresponding to the vertical depth of the middle of the j-producing layer, K; H0 is the vertical depth of the formation temperature measurement point, m; T0 is the original formation temperature corresponding to H0, K; D T is the regional geothermal gradient, K / m.

[0007] The natural gas deviation coefficient is obtained from the natural gas high-pressure physical property test. Generally, the natural gas high-pressure physical properties of the same gas reservoir in the same region are similar. The relationship between the natural gas deviation coefficient and pressure Z = f(p g ), where p g is the pressure of the gas in its state, MPa; Z is the corresponding natural gas deviation coefficient, a decimal.

[0008] After a period of gas well production, the volume of gas produced from a certain production layer under ground conditions is calculated using the following formula: Where: V j采 is the volume of gas produced from the j production layer under ground conditions, m 3 ; p ij is the original formation pressure corresponding to the vertical depth of the middle part of the j-producing layer, MPa; r j is the gas release radius of the j-producing layer, m; r w is the wellbore radius, m; is the porosity of the j-producing layer, decimal; h ij is the thickness of the j-producing layer, m; S gij is the original gas saturation of the j producing layer, decimal.

[0009] When multiple production layers are produced together, the cumulative production volume of the gas well is expressed by the following calculation formula: G p = V j1采 + V j2采 + …+ V jn采 (5) Where: G p is the cumulative production of gas wells, m 3 ; V j1采 、V j2采 、V jn采 are the volumes of gas produced from the j1, j2, and jn production layers under ground conditions, m 3 .

[0010] Substituting (4) into (5), we can obtain: Where: Z ij1 , Z ij2 and Z ijn are the natural gas deviation coefficients at the original formation pressure of the j1, j2, and jn production layers, respectively; p ij1 、p ij2 and p ijnare the original formation pressures corresponding to the vertical depths of the middle of the j1, j2, and jn pay layers, MPa; p j1 、p j2 and p jn are the current formation pressure corresponding to the vertical depth of the middle of the j1, j2, and jn production layers, MPa; T ij1 、T ij2 and T ijn are the original formation temperatures corresponding to the vertical depths of the middle producing layers of j1, j2, and jn, respectively, K; r j1 、r j2 and r jn are the gas leakage radii of the j1, j2, and jn production layers, m; and are the porosity of the j1, j2, and jn production layers, respectively, in decimals; h ij1 、h ij2 and h ijn They are the thickness of the production layers j1, j2 and jn, m; S gij1 , S gij2 and S gijn They are the original gas saturations of the j1, j2 and jn producing layers respectively.

[0011] Compared with the gas leakage radius, the wellbore radius is much smaller than the gas leakage radius, that is, r w <<r j , simulation calculations show that when the deflation radius r j When the shaft radius is greater than 40m, w The impact on the calculation results is less than 1 percentage point and can be ignored in engineering calculations. Formula (6) can be simplified to: Where: G' p is the cumulative production of gas wells, m 3 ; So far, the cumulative gas production volume G' has been established. p Relationship with the deflation radius.

[0012] The relationship between the natural gas deviation coefficient and pressure is Z = f(p g ) is substituted into formula (7); in the formula, only the leakage radius r j1 、r j2 ……r jnis unknown. Solving equation (7), the relationship between the gas leakage radii can be established, so that equation (7) can be transformed into a single-variable equation. To this end, the relationship between the gas leakage radius and the reservoir permeability is statistically analyzed using the gas reservoir engineering method. The ratio of the gas leakage radii of each production layer can be determined according to the proportional relationship of the reservoir permeability of each production layer, so that equation (7) can be transformed.

[0013] For example, in the Carboniferous gas reservoir in eastern Sichuan, the reservoir permeability and the gas leakage radius have a double logarithmic relationship: lnr1=0.6026lnK1+6 (8) Where: r1 is the gas leakage radius of Carboniferous gas reservoir in eastern Sichuan, m; K1 is the reservoir permeability of the Carboniferous gas reservoir in eastern Sichuan, mD.

[0014] For example, in the tight sandstone gas reservoir in the Bohai Bay Basin, the reservoir permeability and the gas leakage radius have a double logarithmic relationship: lnr2=0.04571lnK2+5.4933 (9) Where: r2 is the gas leakage radius of the tight sandstone gas reservoir in the Bohai Bay Basin, m; K2 is the reservoir permeability of the tight sandstone gas reservoir in the Bohai Bay Basin, mD.

[0015] For example, for the tight gas reservoir in the Yan'an gas field in the Ordos Basin, the leakage radius is logarithmically related to the product of the reservoir permeability and the square of the sand addition intensity: r=110.77ln(K*D 2 )+80.356 (10) R 2 =0.9216 (11) Where: r is the gas leakage radius of the tight gas reservoir in Yan'an Gas Field, Ordos Basin, m; K is the reservoir permeability of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, mD; D is the sand adding strength, m 3 / m; R 2 is the coefficient of determination, a decimal.

[0016] Taking the tight gas reservoir of Yan'an gas field in Ordos Basin as an example, we can get: r j1 =110.77ln(K j1 *D j1 2 )+80.356 (12) r j2 =110.77ln(K j2 *D j2 2 )+80.356 (13) rjn =110.77ln(K jn *D jn 2 )+80.356 (14) Where: r j1 、r j2 and r j3 is the gas leakage radius of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, m; K j1 , K j2 and K jn is the reservoir permeability of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, mD; D j1 , D j2 and D jn is the sand adding intensity of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, m 3 / m.

[0017] Formula (12) and formula (13) are transformed into: Formula (12) and formula (14) are transformed into: Substituting equations (15) and (16) into equation (7), we obtain: Formula (17) is only related to r j1 The related quadratic equation can be solved by taking positive value to obtain the gas leakage radius r of the j1 production layer of the tight gas reservoir in Yan'an gas field in the Ordos Basin. j1 ; Then, the gas leakage radius of the j2, ..., jn production layers is obtained through equations (15) and (16), and the gas leakage radius calculation is completed.

[0018] The technical effects of the present invention are: The present invention is based on the principle of material balance, and establishes the relationship between the cumulative production of metered gas wells and the gas leakage radius of each production layer; establishes a relationship between the reservoir permeability and the gas leakage radius, and regresses to obtain the relationship between the gas leakage radius of each production layer and the reservoir permeability, and then constructs the relationship between the gas leakage radii of each production layer, and converts the relationship between the cumulative production of metered gas wells and the gas leakage radius of each production layer into a one-variable equation with the gas leakage radius of a certain production layer, and then solves the gas leakage radius of a certain production layer, and then solves the gas leakage radius of the remaining production layers according to the relationship between the gas leakage radii of each production layer. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is the relationship diagram between the reservoir permeability, gas leakage radius and sand addition intensity of the tight gas reservoir in the Yan'an gas field in the Ordos Basin.

[0020] Figure 2 This is the high-pressure physical property map of the Upper Paleozoic natural gas in the Y12 well area.

[0021] Figure 3 This is the production curve of well Y1201S.

[0022] Figure 4 This is a comparison chart of the calculation results of the deflation radius. DETAILED DESCRIPTION Specific embodiments

[0023] A method for calculating the stratified gas leakage radius of a combined production gas reservoir is as follows: Obtain the basic parameters of each production layer in the target well area, and obtain the current formation pressure p corresponding to the vertical depth of the middle of each production layer according to formula (2-1) j According to formula (2-2), the original formation pressure p corresponding to the vertical depth in the middle of each production layer is obtained ij According to formula (3), the original formation temperature T corresponding to the vertical depth of the middle of each production layer is obtained: ij ; Construct the measurement of the cumulative gas well production G' p The relationship between the gas leakage radius of each production layer is (7); Solve equation (7): Establish the relationship between the gas leakage radius of each production layer and the relationship between the natural gas deviation coefficient and pressure Z = f (p g ), substitute into formula (7) to transform formula (7) into the cumulative production volume of the metered gas well G' p The relationship equation between the gas leakage radius of each production layer is constructed, and the relationship between the gas leakage radius of each production layer is converted into a one-variable equation with the gas leakage radius of a certain production layer, and then the gas leakage radius of a certain production layer is solved, and then the gas leakage radius of the remaining production layers is solved according to the relationship between the gas leakage radius of each production layer.

[0024] Specific experimental example: Well Y1201S in the Y12 well area of ​​Yan'an gas field was put into development in January 2016. The perforated layers are He 8, Shan 1, Shan 2 and Benxi formation. The vertical depth, thickness, porosity, permeability and gas saturation of each production layer are obtained according to the well logging interpretation. The vertical depth H of the original formation pressure measurement point is obtained according to the gas test results. pi is 2591m, corresponding to the original formation pressure p i is 19.70 MPa. According to formula (2-2), the original formation pressure p of He 8, Shan 1, Shan 2 and Benxi Formation is calculated. ij1 、p ij2 、p ij3 、p ij4 They are 19.48MPa, 19.70MPa, 20.10MPa and 20.76MPa respectively. On July 16, 2024, the vertical depth H of the current formation pressure measurement point was obtained based on the gas test results. p is 2612m, corresponding to the current formation pressure pj is 7.17 MPa. According to formula (2-1), the current formation pressure p of He 8, Shan 1, Shan 2 and Benxi Formation is calculated. j1 、p j2 、p j3 、p j4 The vertical depth H0 of the formation temperature measurement point is 2591m, the formation temperature T0 is 359.25K, and the regional geothermal gradient D T is 0.0275 K / m. According to formula (3), the original formation temperature T corresponding to the He 8th, Shan 1st, Shan 2nd and Benxi formations can be obtained. ij1 、T ij2 、T ij3 、T ij4 They are 358.46K, 359.25K, 360.71K, and 363.10K respectively; the sand addition strength D of each production layer is calculated in the summary of fracturing operation jn ; The relationship between the natural gas deviation coefficient and pressure in the regression of high-pressure physical property data is shown in Figure 2 , the regression formula is: Z=0.000228p 2 -0.00622p+0.975913 (18) According to the above data sources, the parameters of each production layer of Well Y1201S are statistically shown in Table 1; Table 1 Statistics of parameters of each production layer in Y1201S well Since it was put into production, the production curve of Y1201S well is as follows: Figure 3 . Three gas production profile tests were completed on August 12, 2021, August 10, 2022, and July 16, 2024. The test results are detailed in Table 2. The cumulative production volume of gas wells measured on August 12, 2021, August 10, 2022, and July 16, 2024 G' p They are 16.7819 million cubic meters, 20.4421 million cubic meters, and 26.9925 million cubic meters, respectively. Based on the cumulative gas production and profile test results, the gas leakage radius of each layer is obtained by splitting and calculating as a comparison basis for the calculation results of the method of the present invention to verify the reliability of the method; Table 2 Statistical table of gas production profile test results of Y1201S well In this specific experimental example, box 8 is j1, mountain 1 is j2, mountain 2 is j3, and Benxi is j4. The cumulative production volume G' of the metered gas well on July 16, 2024 is calculated. p The gas leakage radius of each production layer is 26.9925 million cubic meters.

[0026] Substituting the relevant parameters in Table 1 into equations (15) and (16), we can obtain: The calculation results are: r j2 =0.8418 r j1 (twenty two) r j3 =0.9748 r j1 (twenty three) r j4 =1.5560 r j1 (twenty four) Substituting the parameters in Table 1, equation (18), equation (22), equation (23) and equation (24) into equation (17), we obtain: Find the solution of formula (25) and take the positive value as: r j1 =293.18m (26) Substituting formula (26) into formula (22), formula (23) and formula (24) respectively, we get: r j2 =254.01m, r j3 =258.63m, r j4 =469.51m( Figure 4 ).

[0027] The method recognized by the industry as being relatively accurate in calculating the stratified gas leakage radius is the gas production profile calculation method. This embodiment uses the stratified gas leakage radius calculated by the gas production profile method as a comparison basis to verify the reliability of the calculation results of the present invention. First, the cumulative production of each layer is split according to the gas production profile, and the stratified dynamic reserves are calculated. The volumetric method of reserve calculation is applied in reverse to obtain the gas leakage radius r. j1 、r j2 、r j3 and r j4 They are 263.22m, 254.38m, 271.43m, 457.52m respectively. Figure 4 ).

[0028] The r calculated by the method of the present invention j1 、r j2 、r j3 and r j4 The gas leakage radius errors compared with those calculated by the gas production profile method are -11.38%, 0.14%, 4.71%, and -2.62% respectively. Figure 4 ). The calculation results are relatively similar, with small errors, and can fully meet the engineering technical requirements.

Claims

1. A method for calculating the stratified gas leakage radius of a combined production gas reservoir, characterized in that: Here’s how: Obtain the basic parameters of each production layer in the target well area, and then obtain the original formation pressure, current formation pressure and original formation temperature corresponding to the vertical depth of the middle of each production layer; The cumulative gas production volume G of the measuring gas well is constructed by the following formula (7): ’ p Relationship with the gas leakage radius of each production layer: Where: G ’ p is the cumulative production of gas wells, m 3 ; Z ij1 , Z ij2 and Z ijn They are the natural gas deviation coefficients under the original formation conditions of the j1, j2, and jn production layers, respectively, in decimals; p ij1 、p ij2 and p ijn are the original formation pressures corresponding to the vertical depths of the middle producing layers of j1, j2, and jn, MPa; p j1 、p j2 and p jn are the current formation pressure corresponding to the vertical depth of the middle of the j1, j2, and jn production layers, MPa; Z sc is the natural gas deviation coefficient under ground standard conditions, decimal; T sc is the temperature under standard ground conditions, K; p sc is the pressure under standard ground conditions, MPa; T ij1 , T ij2 and T ijn are the original formation temperatures corresponding to the vertical depths of the middle producing layers of j1, j2, and jn, respectively, K; r j1 、r j2 and r jn are the gas leakage radii of the j1, j2, and jn production layers, m; and are the porosity of the j1, j2, and jn production layers, respectively, in decimals; h ij1 、h ij2 and h ijn They are the thickness of the production layers j1, j2 and jn, m; S gij1 , S gij2 and S gijn They are the original gas saturation of j1, j2 and jn production layers respectively; The relationship between the gas leakage radius of each production layer and the relationship between the natural gas deviation coefficient and pressure are established, and then substituted into formula (7) to transform formula (7) into a relationship equation about the gas leakage radius of each production layer, and then the gas leakage radius of each production layer is solved.

2. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 1, characterized in that: The specific solution process of the current formation pressure corresponding to the vertical depth in the middle of each production layer is: p j = p / H p ·H j (2-1) Where: p j is the current formation pressure corresponding to the vertical depth of the middle of the j-producing layer, MPa; H p is the vertical depth of the current formation pressure measurement point, m; p is H p Current formation pressure corresponding to vertical depth, MPa; H j is the vertical depth corresponding to the middle of the j-producing layer, m; The specific solution process of the original formation pressure corresponding to the vertical depth in the middle of each production layer is: p ij = p i / H pi ·H j (2-2) Where: p ij is the original formation pressure corresponding to the vertical depth of the middle part of the j-producing layer, MPa; H pi is the vertical depth of the original formation pressure measurement point, m; p i H pi Original formation pressure corresponding to vertical depth, MPa.

3. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 1, characterized in that: The specific solution process of the original formation temperature corresponding to the vertical depth of each production layer is: T ij = T0+( H j -H0)D T (3) Where: T ij is the original formation temperature corresponding to the vertical depth of the middle of the j-producing layer, K; H0 is the vertical depth of the formation temperature measurement point, m; T0 is the original formation temperature corresponding to H0, K; D T is the regional geothermal gradient, K / m.

4. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 1, characterized in that: The specific process of converting formula (7) into a one-variable equation for solution is as follows: establish the relationship between reservoir permeability and gas leakage radius; regress to obtain the relationship between the gas leakage radius of each production layer and the reservoir permeability, and then construct the relationship between the gas leakage radius of each production layer, convert formula (7) into a one-variable equation with the gas leakage radius of a certain production layer, and then solve the gas leakage radius of a certain production layer, and then solve the gas leakage radius of the remaining production layers according to the relationship between the gas leakage radii of each production layer.

5. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 4, characterized in that: For Carboniferous gas reservoirs in eastern Sichuan, the reservoir permeability and gas leakage radius have a double logarithmic relationship, specifically: lnr1=0.6026lnK1+6 (8) Where: r1 is the gas leakage radius of Carboniferous gas reservoir in eastern Sichuan, m; K1 is the reservoir permeability of the Carboniferous gas reservoir in eastern Sichuan, mD.

6. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 4, characterized in that: In the tight sandstone gas reservoirs in the Bohai Bay Basin, the reservoir permeability and the gas leakage radius have a double logarithmic relationship, specifically: lnr2=0.04571lnK2+5.4933 (9) Where: r2 is the gas leakage radius of the tight sandstone gas reservoir in the Bohai Bay Basin, m; K2 is the reservoir permeability of the tight sandstone gas reservoir in the Bohai Bay Basin, mD.

7. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 4, characterized in that: For the tight gas reservoir in Yan'an Gas Field in the Ordos Basin, the leakage radius is logarithmically related to the product of the reservoir permeability and the square of the sand addition intensity, specifically: r=110.77ln(K*D 2 )+80.356 (10) R 2 ＝0.9216 (11) Where: r is the gas leakage radius of the tight gas reservoir in Yan'an Gas Field, Ordos Basin, m; K is the reservoir permeability of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, mD; D is the sand adding strength, m 3 / m; R 2 is the coefficient of determination, a decimal.

8. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 7, characterized in that: In the tight gas reservoir of Yan'an Gas Field in the Ordos Basin, the relationship between the gas leakage radius of each production layer and the reservoir permeability and the square of the sand addition intensity is obtained by regression, which is specifically: r j1 =110.77ln(K j1 *D j1 2 )+80.356 (12) r j2 =110.77ln(K j2 *D j2 2 )+80.356 (13) r jn =110.77ln(K jn *D jn 2 )+80.356 (14) Where: r j1 、r j2 and r j3 is the gas leakage radius of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, m; K j1 , K j2 and K jn is the reservoir permeability of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, mD; D j1 , D j2 and D jn is the sand adding intensity of the j1, j2 and j3 production layers of the tight gas reservoir in the Yan'an gas field in the Ordos Basin, m 3 / m.

9. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 8, characterized in that: According to the relationship between the gas leakage radius and the reservoir permeability, the relationship between the gas leakage radius of each production layer is constructed, which is as follows: Formula (12) and formula (13) are transformed into: Formula (12) and formula (14) are transformed into: That is, construct the gas leakage radius and r of each production layer j1 The relationship formula.

10. The method for calculating the stratified gas leakage radius of a combined production gas reservoir according to claim 9, characterized in that: Transform equation (7) into a one-dimensional equation for the gas leakage radius of a certain production layer, as follows (17): Formula (17) is only related to r j1 The related quadratic equation can be solved by taking a positive value to obtain the gas leakage radius r of the j1 production layer of the tight gas reservoir in the Yan'an gas field in the Ordos Basin. j1 Then, the gas leakage radius of the j2, ..., jn production layers is obtained by using equations (15) and (16), and the gas leakage radius calculation is completed.

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