A method for calculating a reasonable gas production rate of a gas storage

Abstract

This invention discloses a method for calculating the reasonable gas extraction rate of a gas storage facility. Step S1: Given the wellhead pressure P wh Initial values ​​of deviation coefficient Z0, reasonable gas production rate q0, and corresponding bottom hole flowing pressure P. wf0 S2, Calculate relevant parameter values; S3, Calculate gas production capacity q g and the corresponding bottom hole flowing pressure P wf S4, Determine q g Between q0 and P wf With P wf0 Does the absolute difference between them simultaneously satisfy less than 0.00001? If not, change q. g and P wf Substitute S2 and S3 to calculate the new q g1 and P wf1 Repeat the iteration until the absolute difference requirement is met; S5, the q calculated in the last iteration. gn and P wfn That is, wellhead pressure P wh The reasonable gas production rate and its corresponding bottom hole flowing pressure; S6, repeat S1-S5 to calculate different wellhead pressures P. wh Under the given conditions, determine the reasonable gas production rate and its corresponding bottom hole flowing pressure; S7, calculate the critical sand production rate q. sc S8, according to q sc The appropriate gas production rate is selected from the calculation results of S5 and S6. This invention can accurately calculate the reasonable gas production capacity of each injection and production well under the wellhead pressure and formation pressure.

Description

Technical Field

[0001] This invention relates to the field of gas extraction technology for gas storage facilities, and in particular to a method for achieving a reasonable gas extraction rate in gas storage facilities. Background Technology

[0002] Determining the optimal gas production rate for a gas storage facility is crucial for guiding peak shaving. The traditional method for determining this rate involves plotting the Inflow Dynamic Rate (IPR) and Outflow Dynamic Rate (OPR) curves on the same graph. The intersection of the IPR and OPR curves is then used; the horizontal axis of the intersection represents the optimal gas production capacity, and the vertical axis represents the corresponding bottomhole flowing pressure. A more specific method involves plotting the IPR curves under different formation pressures and the OPR curves under different wellhead pressures on the inflow / outflow curve chart to obtain the optimal gas production rate for that formation and wellhead pressure. Figure 1 As shown, to the left of point A, for example, at a production rate of q1, the bottomhole flowing pressure p1 > p3, indicating that the inflow capacity within the production system is greater than the outflow capacity. This suggests that the design capacity of the tubing or outflow pipeline equipment system is too small, or that there are factors hindering flow in the outflow section, limiting the gas well's production capacity. To the right of point A, for example, at a production rate of q2, the situation is reversed. This indicates that the gas layer's production capacity does not reach the designed outflow pipeline system's capacity, suggesting that the designed outflow pipeline capacity is too large, causing unnecessary waste, or that certain parameters of the gas well are not properly controlled, or that gas layer damage reduces the well's production capacity, requiring unblocking, modification, or other measures. Only at point A is the production capacity of the producing layer exactly equal to the production capacity of the outflow pipeline system. This indicates that the well is in a state of coordinated inflow and outflow capacity. This point is called the coordinated production point, which is the maximum daily gas production of the gas well, and is also selected as the reasonable gas production capacity of the gas well. According to the definition of reasonable gas production capacity, at this point, the inflow capacity equals the outflow capacity, i.e., q... in =q out .

[0003] Traditional methods can determine the optimal gas production rate and its bottom hole flowing pressure. However, determining each set of optimal gas production rates and bottom hole flowing pressures requires plotting two curves and calculating a large amount of data; moreover, it is impossible to plot a continuous optimal gas production capacity curve, only a series of points can be determined; and there are errors in reading the coordinates, making it impossible to obtain an accurate optimal gas production rate and its corresponding bottom hole flowing pressure. Summary of the Invention

[0004] To address the aforementioned shortcomings of traditional methods for determining the optimal gas extraction rate for gas storage facilities, this invention provides a method for calculating the optimal gas extraction rate for gas storage facilities.

[0005] The method for calculating the reasonable gas extraction rate of a gas storage facility provided by this invention comprises the following steps:

[0006] S1. Set the wellhead pressure P according to the site conditions. wh Under this wellhead pressure condition, given an initial value of the deviation coefficient Z0, an initial value of the reasonable gas production rate q0, and a corresponding initial value of the bottom hole flowing pressure P... wf0 .

[0007] S2, given q0, P wf0 Given the state, calculate the following parameters:

[0008] Average temperature of the static air column in the wellbore Dimensionless exponent S, friction coefficient f, gas flow Reynolds number Re, wellbore velocity v, natural gas volume factor B g Average pressure of the static air column in the wellbore Natural gas viscosity μ g Natural gas density ρ g Natural gas deviation coefficient Z.

[0009] (1) Average temperature of the static air column in the wellbore The calculation formula is as follows:

[0010]

[0011] In the formula, T wf T wh , These are the bottom hole temperature, wellhead temperature, and average temperature of the static gas column in the wellbore, respectively, in K.

[0012] (2) The formula for calculating the dimensionless exponent S is:

[0013]

[0014] In the formula, γ g ρ is the relative density of natural gas, dimensionless; h is the depth from the wellhead to the middle of the gas layer, in meters. This is the average deviation coefficient of the static gas column in the wellbore.

[0015] (3) The friction coefficient is derived using the formula proposed by Jain in 1976:

[0016]

[0017] That is, the friction coefficient f is:

[0018]

[0019] In the formula, e / D is the relative roughness, which is the absolute roughness e / pipe diameter D. Recommended roughness is e = 0.016 mm; R e It is the Reynolds number.

[0020] (4) Reynolds number R e for:

[0021]

[0022] In the formula, ρ g The density of natural gas is kg / m³. 3 v is the wellbore flow velocity, m / s; D is the tubing inner diameter, m; μ g ρ represents the viscosity of natural gas, in mPa·s.

[0023] (5) The formula for calculating the flow velocity v in the wellbore is:

[0024]

[0025]

[0026] In the formula, q gc The natural gas flow rate under standard conditions, m 3 / d;B g is the natural gas volume factor, a decimal; M is the wellbore cross-sectional area, in meters. 2 Z represents the natural gas deviation coefficient. The average temperature of the static gas column in the wellbore; This represents the average pressure of the static gas column in the wellbore.

[0027] (6) Average pressure of the static gas column in the wellbore The calculation formula is:

[0028]

[0029] In the formula, P wf P wh These are the bottom-hole flowing pressure and the wellhead static pressure, respectively, in MPa.

[0030] (7) The natural gas deviation coefficient Z is calculated iteratively according to the Cranmer method.

[0031]

[0032] In the formula, P pr To simulate the pressure; T pr For comparison temperature; P pc The quasi-critical pressure; T pc denoted as quasi-critical temperature; T is the wellbore temperature; P is the wellbore pressure, in MPa.

[0033] (8) Natural gas viscosity μ g Calculated using the Lee-Gonzalez-Eakin semi-empirical method.

[0034]

[0035] In the formula, Mg is the average molecular weight of natural gas; T is the wellbore temperature, °C.

[0036] (9) Natural gas density ρ g The calculation formula is:

[0037]

[0038] In the formula, γ g The relative density of natural gas is dimensionless. This is the average deviation coefficient of the static gas column in the wellbore; The average temperature of the static gas column in the wellbore; This represents the average pressure of the static gas column in the wellbore.

[0039] S3. Using the calculated parameters and well test data (testing formation pressure P) Rc Test the bottom hole flowing pressure P wfc Test output Q gc Substitute these values ​​into the following two formulas to calculate the gas production capacity q. g and the corresponding bottom hole flowing pressure P wf :

[0040]

[0041]

[0042] in,

[0043] In the formula, P R denoted as formation pressure, e as absolute roughness, D as tubing inner diameter (m); A and B are coefficients of the binomial productivity equation.

[0044] In actual production, using well test data to calculate production capacity is more accurate. Therefore, this invention derives a method for calculating the coefficients A and B of the binomial production capacity equation based on well test data, according to Chen Yuanqian's one-point method for calculating production capacity.

[0045] The test formation pressure P of a gas well can be obtained through production testing. Rc Test the bottom hole flowing pressure P wfc Test output Q gc The calculation methods for A and B can be derived from the basic equation of the binomial productivity equation as follows:

[0046]

[0047]

[0048] There are many methods for calculating the coefficients of the binomial productivity equation. In practical applications, the appropriate method can be selected according to the different types of gas wells.

[0049] S4, Comparison with q g and q0, P wf and P wf0 Determine q g The absolute difference between q0 and P wf With P wf0 Does the absolute difference between them simultaneously satisfy the condition that it is less than 0.00001? If not, then q g and P wf Substitute these parameters into step S2 and recalculate them; then proceed to step S3 to calculate the new q. g1 and P wf1 Then compare q g1 and q g P wf1 and P wf Determine q g1 With q g The absolute difference between them, P wf1 With P wf Check whether the absolute difference between them is simultaneously less than 0.00001; repeat this iteration until both absolute differences are less than 0.00001.

[0050] S5. Output q calculated in the last iteration. gn and P wfn That is, wellhead pressure P wh The reasonable gas production rate and its corresponding bottom hole flowing pressure.

[0051] S6. Change the given wellhead pressure P wh By repeating steps S1-S5, the different wellhead pressures P can be calculated. wh The reasonable gas production rate under the given conditions and its corresponding bottom hole flowing pressure.

[0052] S7, based on formation pressure P R The critical sand production rate q under this formation pressure is calculated from the critical sand production pressure difference Δp. sc :

[0053]

[0054] S8. The critical sand discharge flow rate q calculated in S7. sc Based on the screening criteria: the reasonable gas production rate should not exceed the critical sand discharge flow rate q. sc The optimal reasonable gas extraction rate is selected from the reasonable gas production rates calculated in steps S5 and S6.

[0055] The calculation method of the present invention may further include step S9: based on the critical sand discharge flow rate q calculated in S7. sc With formation pressure P RCalculate the wellhead pressure P under the corresponding formation pressure and flow rate. whsc :

[0056]

[0057] In the formula, S is the average temperature of the static air column in the wellbore, S is the dimensionless exponent, and f is the friction coefficient. The average pressure of the static air column in the wellbore, P wf Here, e is the bottom hole flowing pressure, e is the absolute roughness, D is the tubing inner diameter, and m and Z are the natural gas deviation coefficients.

[0058] Compared with the prior art, the advantages of the present invention are:

[0059] (1) The method of the present invention can accurately calculate the reasonable gas production capacity under each wellhead pressure and formation pressure, without the need to draw gas injection and gas production charts and determine the reasonable gas production capacity by reading the intersection points.

[0060] (2) By comparing the calculation results with the injection and production chart data, it was found that the calculation results were quite close. According to the definition and derivation process of reasonable production rate, the reasonable production capacity calculated by this method is the accurate value. Compared with the injection and production capacity chart, it greatly reduces the error in calculating reasonable production capacity.

[0061] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0062] Figure 1 Inflow and outflow dynamic curves.

[0063] Figure 2 The inflow and outflow dynamic curves drawn using traditional methods. Detailed Implementation

[0064] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0065] The method for calculating the reasonable gas extraction rate of a gas storage facility provided by this invention was applied to a specific case to calculate the reasonable gas extraction capacity and the corresponding bottom hole flowing pressure under different wellhead pressure conditions.

[0066] For example, at a formation pressure of 34 MPa, the reasonable gas production capacity and corresponding bottom hole flowing pressure were calculated under different wellhead pressures (26, 24, 22, 20, 18, 16, 14 MPa). The values ​​of each parameter and the calculation results are shown in Table 1-4.

[0067] Table 1. Values ​​of relevant parameters

[0068]

[0069] Table 2. Values ​​of relevant parameters

[0070]

[0071] Additionally, for parameters with the same values ​​under different wellhead pressures, such as: gas layer depth h = 3578.14m, bottom hole temperature T... wf =88.26℃, wellhead temperature T wh =40℃, average temperature relative density γ g =0.5958, K=129.3478, X=5.2865, Y=1.3427, tubing inner diameter D=0.09956m, cross-sectional area M=0.0078m² 2 .

[0072] Table 3. Basic Data Table for Well Testing

[0073] <![CDATA[Formation pressure P Rc > <![CDATA[Bottomhole flowing pressure P wfc > <![CDATA[Output Q gc > A B MPa MPa <![CDATA[10 4 m 3 / d]]> —— —— 33.474 32.072 27.674 2.061350369 0.045504563

[0074] Table 4. Values ​​and Calculation Results of Relevant Parameters

[0075]

[0076] The critical sand production pressure difference needs to be measured based on sand production experiments. The emergency gas production capacity and the converted wellhead pressure are calculated with a critical sand production pressure difference of 4 MPa.

[0077] The results of the calculated reasonable gas extraction capacity and reasonable production pressure difference using the above method are shown in Table 5.

[0078] Table 5. Calculation Results of Reasonable Gas Extraction Capacity, Reasonable Production Pressure Difference, and Emergency Gas Extraction Capacity

[0079]

[0080]

[0081] The reasonable gas extraction capacity in the calculation results should not exceed the emergency gas extraction capacity. Therefore, some data that do not meet the requirements should be discarded in the calculation results in Table 5. The final calculation results are shown in Table 6.

[0082]

[0083] Inflow-outflow dynamic curves plotted using traditional methods, such as Figure 2As shown in the figure, comparing the injection-production chart and the calculation results using the method of this invention reveals that the reasonable gas production capacity calculated by the method of this invention corresponds to the coordination point of the injection-production chart in both cases, and the calculation results are quite close. Furthermore, according to the definition and derivation process of the reasonable gas production rate, only the reasonable gas production capacity calculated using this method is an accurate value, significantly reducing the error in calculating the reasonable gas production capacity compared to the injection-production chart. This demonstrates that the method of this invention can accurately calculate the reasonable gas production capacity under various wellhead pressures and formation pressures, eliminating the need to draw injection and production charts and determine the reasonable gas production capacity by reading the intersection points. Simultaneously, it utilizes emergency gas production rates to select suitable reasonable gas production rates.

[0084] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calculating the reasonable gas extraction rate of a gas storage facility, characterized in that, The steps are as follows: S1. Set the wellhead pressure P according to the site conditions. wh Under this wellhead pressure condition, given an initial value of the deviation coefficient Z0, an initial value of the reasonable gas production rate q0, and a corresponding initial value of the bottom hole flowing pressure P... wf0 ; S2, given q0, P wf0 Given the state, calculate the following parameters: Average temperature of the static air column in the wellbore Dimensionless exponent S, friction coefficient f, gas flow Reynolds number Re, wellbore velocity v, natural gas volume factor B g Average pressure of the static air column in the wellbore Natural gas viscosity μ g Natural gas density ρ g Natural gas deviation coefficient Z; S3. Substitute the calculated parameters and well test data into the following two formulas to calculate the gas production capacity q. g and the corresponding bottom hole flowing pressure P wf : in, In the formula, P R For formation pressure, e represents the absolute roughness. D is the inner diameter of the oil pipe, in meters; A and B are the coefficients of the binomial capacity equation; S4, Comparison with q g and q0, P wf and P wf0 Determine q g The absolute difference between q0 and P wf With P wf0 Does the absolute difference between them simultaneously satisfy the condition that it is less than 0.00001? If not, then q g and P wf Substitute these parameters into step S2 and recalculate them; then proceed to step S3 to calculate the new q. g1 and P wf1 Then compare q g1 and q g P wf1 and P wf Determine q g1 With q g The absolute difference between them, P wf1 With P wf Check whether the absolute difference between them is simultaneously less than 0.00001; repeat this iteration until both absolute differences are less than 0.00001. S5. Output q calculated in the last iteration. gn and P wfn Wellhead pressure P wh The reasonable gas production rate and its corresponding bottom hole flowing pressure; S6. Change the given wellhead pressure P wh Repeat steps S1-S5 to calculate different wellhead pressures P. wh The reasonable gas production rate under the given conditions and its corresponding bottomhole flowing pressure; S7, based on formation pressure P R The critical sand production rate q under this formation pressure is calculated from the critical sand production pressure difference Δp. sc : S8. The critical sand discharge flow rate q calculated in S7. sc Based on the screening criteria: the reasonable gas production rate should not exceed the critical sand discharge flow rate q. sc The optimal reasonable gas extraction rate is selected from the reasonable gas production rates calculated in steps S5 and S6.

2. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the average temperature of the static gas column in the wellbore... The calculation formula is as follows: In the formula, T wf T wh , These are the bottom hole temperature, wellhead temperature, and average temperature of the static gas column in the wellbore, respectively, in K.

3. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 2, characterized in that, In step S2, the formula for calculating the dimensionless exponent S is: In the formula, γ g ρ is the relative density of natural gas, dimensionless; h is the depth from the wellhead to the middle of the gas layer, in meters. This is the average deviation coefficient of the static gas column in the wellbore.

4. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the formula for calculating the wellbore flow velocity v is: In the formula, q gc The natural gas flow rate under standard conditions, m 3 / d;B g M is the natural gas volume factor, a decimal; M is the wellbore cross-sectional area, in meters. 2 Z represents the natural gas deviation coefficient. The average temperature of the static gas column in the wellbore; This represents the average pressure of the static gas column in the wellbore.

5. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the average pressure of the wellbore static gas column The calculation formula is: In the formula, P wf P wh These are the bottom-hole flowing pressure and the wellhead static pressure, respectively, in MPa.

6. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the natural gas deviation coefficient Z is calculated iteratively according to the Cranmer method.

7. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the viscosity μ of natural gas g Calculated using the Lee-Gonzalez-Eakin semi-empirical method.

8. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, In step S2, the density ρ of natural gas g The calculation formula is: In the formula, γ g The relative density of natural gas is dimensionless. This is the average deviation coefficient of the static air column in the wellbore; The average temperature of the static gas column in the wellbore; This represents the average pressure of the static gas column in the wellbore.

9. The method for calculating the reasonable gas extraction rate of a gas storage facility as described in claim 1, characterized in that, It also includes step S9, which involves calculating the critical sand discharge flow rate q in S7. sc With formation pressure P R Calculate the wellhead pressure P under the corresponding formation pressure and flow rate. whsc : In the formula, S is the average temperature of the static air column in the wellbore, S is the dimensionless exponent, and f is the friction coefficient. The average pressure of the static air column in the wellbore, P wf Here, e is the bottom hole flowing pressure, e is the absolute roughness, D is the tubing inner diameter, and m and Z are the natural gas deviation coefficients.

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