Method for obtaining pressure during gas injection in injection and production wells of underground gas storage

Abstract

The present invention relates to the technical field of methods for obtaining gas injection pressure, and is a method for obtaining the pressure during the gas injection process of an injection-production well of an underground gas storage reservoir. The method primarily utilizes the physical properties of the underground gas storage reservoir and field measured data. In the process of calculating the objective function, an improved particle swarm optimization algorithm is used for fitting calculation to obtain the optimal value of the objective function, namely, the optimal values ​​of the reservoir pressure, bottomhole pressure, and wellhead oil pressure. The present invention adopts an improved particle swarm optimization algorithm, which accelerates the convergence of the algorithm by introducing a strategy for automatically calculating the inertia factor and a mutation operation. The method also utilizes the physical properties of the underground gas storage reservoir and field measured data for inversion, and continuously optimizes the permeability and gas supply radius parameters to achieve an optimal fit between the wellhead oil pressure calculated by the model and the measured wellhead oil pressure. By fitting the wellhead oil pressure, the dynamic changes of the bottomhole pressure and reservoir pressure are obtained, thereby helping to guide the safe operation of the underground gas storage reservoir.

Description

Technical Field

[0001] The invention relates to the technical field of methods for obtaining gas injection pressure, in particular to a method for obtaining pressure during the gas injection process of an injection-production well of an underground gas storage reservoir. Background Art

[0002] During the operation of an underground gas storage (UGS), the high-speed injection and withdrawal of gas through injection and production wells causes constant fluctuations in reservoir pressure, potentially disrupting the pressure equilibrium within the UGS. Therefore, real-time monitoring and prediction of reservoir pressure during injection is essential for ensuring the safe operation and improving the efficiency of UGS. Researchers have conducted research on gas storage pressure calculations. For example, Yu Benfu et al. proposed a method for predicting reservoir pressure distribution in gas storage, focusing on the fractal characteristics of the reservoir pore medium and the impact of reservoir pressure changes on the reservoir medium seepage parameters. They also analyzed the effects of different parameters on reservoir pressure, and the calculation results were highly accurate (Prediction of Reservoir Pressure Distribution in Depleted Gas Reservoirs Considering Fractal Characteristics of Reservoir Porosity, Yu Benfu et al., Acta Petrolei Sinica, September 2013, Vol. 34, No. 5). Tang Ligen et al. studied the bottomhole inflow dynamics of gas storage, focusing on the impact of permeability changes on bottomhole inflow dynamics (Prediction of Bottomhole Inflow Dynamics of Gas Reservoirs Converted into Gas Storage Based on Development Data, Tang Ligen et al., Petroleum Exploration and Development, February 2016, Vol. 43, No. 1). Yue Sanqi et al. proposed a method for calculating the bottomhole pressure of gas storage reservoirs, derived the bottomhole pressure calculation equations for underground gas storage reservoirs during the injection and shut-in periods, and used the improved average temperature and average deviation coefficient method, the iterative method, and the point-by-point calculation method to calculate the bottomhole flowing pressure during the injection phase and the bottomhole static pressure during the shut-in phase (Study on Calculation of Bottomhole Pressure of Injection and Production Wells in Underground Gas Storage, Yue Sanqi et al., Oil and Gas Reservoir Evaluation and Development, June 2017, Vol. 7, No. 3). However, they only calculated the reservoir pressure or bottomhole pressure separately, ignoring the relationship between the reservoir pressure, bottomhole pressure, and wellhead oil pressure, and thus were unable to grasp the dynamic changes in the pressure system.

[0003] During the operation of underground gas storage (UGS), the pressure in injection and production wells is constantly changing due to the frequent alternation of injection and production cycles. While pressure is crucial for the safe operation of UGS, dynamic monitoring of both bottomhole and reservoir pressures is not practical. As mentioned above, previous research on UGS pressure calculation has focused solely on bottomhole or reservoir pressure, ignoring the relationship between reservoir, bottomhole, and wellhead oil pressure. Consequently, this approach fails to capture the dynamics of the pressure system.

[0004] Currently, underground gas storage facilities typically only monitor wellhead pressure during operation. Constant monitoring of bottomhole and reservoir pressures is impractical. Therefore, research is needed to calculate the distribution patterns of bottomhole and reservoir pressures to ensure safe operation and improve operational efficiency. Summary of the Invention

[0005] The present invention provides a method for obtaining the pressure during the gas injection process of an injection-production well in an underground gas storage reservoir. This method overcomes the shortcomings of the above-mentioned existing technologies and can comprehensively understand the relationship between reservoir pressure, bottomhole pressure, and wellhead oil pressure. Based on an improved particle swarm optimization algorithm, it can obtain the pressure during the gas injection process of the injection-production well in an underground gas storage reservoir, and then grasp the dynamic changes in the pressure system to ensure the safe operation of the underground gas storage reservoir.

[0006] The technical solution of the present invention is achieved through the following measures: A method for obtaining the pressure during the gas injection process of an injection and production well of an underground gas storage reservoir comprises the following steps:

[0007] Step 1: Calculate the reservoir pressure of the underground gas storage during the gas injection process according to the reservoir pressure calculation method;

[0008] Step 2: Calculate the bottom hole pressure of the injection and production well during the gas injection process according to the bottom hole pressure calculation method;

[0009] Step 3: Calculate the wellhead oil pressure of the injection and production wells during the gas injection process according to the wellhead oil pressure calculation method;

[0010] Step 4: Calculate the objective function and evaluate the quality of the individual;

[0011] Step 5: Using the physical properties of the underground gas storage and field measured data, an improved particle swarm optimization algorithm is used to fit the objective function in the process of calculating the objective function to obtain the optimal value of the objective function, that is, the optimal values ​​of the reservoir pressure, bottom hole pressure, and wellhead oil pressure.

[0012] The physical properties of underground gas storage and field measured data include measured oil pressure, flow pressure and gas production.

[0013] The following are further optimizations and / or improvements to the above technical solutions:

[0014] In the above step 1, the reservoir pressure is calculated as follows:

[0015] The reservoir pressure calculation formula is:

[0016]

[0017] In formula (1), x = Kp0 / φμ;

[0018] Among them, p r is the reservoir pressure at the gas supply boundary, MPa; r is the gas well control radius, m; t is the gas injection time, d; p0 is the initial reservoir pressure, MPa; Q g is the gas injection rate, m 3 / s; μ is viscosity, Pa.s; K is permeability, 10 -3μm 2 ; h is the effective thickness of the reservoir, m; p a is standard atmospheric pressure, Pa; is the natural gas compression factor under formation temperature and average formation pressure; T f is the formation temperature, K; T a is the standard temperature, K; -Ei() is the power integral function; φ is the porosity.

[0019] In the above step 2, the bottom hole pressure is calculated as follows:

[0020] The bottom hole pressure of the injection-production well is calculated using the production equation, and the formula is:

[0021]

[0022] Among them, p wf is the bottom hole flowing pressure, MPa; q g is the gas injection volume of the gas well, 10 4 m 3 / d; A, B are the coefficients of the binomial production capacity equation, MPa 2 / (10 4 m 3 ).

[0023] In step 3 above, the wellhead oil pressure is calculated as follows:

[0024] The calculation method for the wellhead oil pressure of underground gas storage is based on the vertical pipe flow equation of gas flow in the wellbore. The calculation formula is:

[0025]

[0026]

[0027] Among them, P tf is the wellhead oil pressure, MPa; f is the wellbore friction coefficient; q g is the gas injection volume, m 3 / d; d is the inner diameter of the injection and production pipe, m; γ g is the relative density of gas; H is the depth from the wellhead to the middle of the gas layer, m; is the average temperature of the wellbore or well section, K; is the average compressibility factor of the wellbore or well section.

[0028] In the above step 4, the calculation formula of the objective function is:

[0029]

[0030] Among them, p tfi is the calculated wellhead oil pressure on the ith day, MPa; is the corresponding measured wellhead oil pressure, MPa; m is the total number of gas injection days.

[0031] In step 5 above, the steps to improve the particle swarm optimization algorithm include:

[0032] 1) Generate an initial group: randomly generate N individuals as the initial group,

[0033] X id =X imin +(X imax -X imin )·F1 (6)

[0034] Among them, X id represents the position of the dth dimension of the i-th individual; X imin represents the position of the minimum value of the dth dimension of the i-th individual; X imax represents the position of the maximum value of the d-th dimension of the i-th individual; F1 represents the function of generating random numbers in the interval (0,1);

[0035] 2) Calculate the objective function value: Substitute the generated initial population (permeability K, gas supply radius parameter r) as initial conditions into formula (1) to calculate the reservoir pressure of the underground gas storage, then calculate the bottom hole pressure of the injection and production well according to formula (2), and then substitute it into formula (3) to obtain the wellhead oil pressure of the injection and production well, and then calculate formula (5) to obtain the objective function value;

[0036] 3) Update speed and position formula: In the process of calculating the objective function, a strategy of automatically adjusting the inertia factor is introduced to adjust the global and local optimization performance, thereby achieving the effect of accelerating convergence and saving time.

[0037]

[0038] V id =ω·V id +2·F1·(P id -X id )+2·F1·(P gd -X id ) (8)

[0039] X id =X id +V id (9)

[0040] Among them, ω represents the automatic adjustment inertia factor, f i represents the objective function value of the i-th individual, f min represents the minimum value of the objective function, represents the average value of the objective function;

[0041] 4) Mutation operation: Introduce the mutation operation, randomly select the dth dimension of the i-th individual to mutate, and increase the diversity of the population;

[0042] X id =X id +F2 (10)

[0043] Among them, F2 represents a function that generates random numbers in the interval (-1,1);

[0044] Repeat steps 2) to 4) until the individual performance in the population meets the convergence requirements. At this time, the global optimal individual of the population is the optimal value of the objective function, that is, the optimal values ​​of reservoir pressure, bottom hole pressure, and wellhead oil pressure.

[0045] This paper employs an improved particle swarm optimization algorithm, accelerating its convergence by introducing a strategy for automatically calculating the inertia factor and a mutation operation. Inversion is performed using underground gas storage reservoir physical properties and field-measured data. By continuously optimizing permeability and gas supply radius parameters, the model-calculated wellhead oil pressure achieves an optimal fit with the measured wellhead oil pressure. By fitting the wellhead oil pressure, the dynamic changes in bottomhole and reservoir pressures are determined, helping to guide the safe operation of underground gas storage reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Attachment Figure 1 This is a flow chart of the improved particle swarm optimization algorithm described in the present invention.

[0047] Attachment Figure 2a This is a locally enlarged comparison diagram of the convergence curves obtained in the early iterations of the improved particle swarm optimization algorithm and the basic particle swarm optimization algorithm.

[0048] Attachment Figure 2b Comparison of the convergence curves obtained by the improved particle swarm optimization algorithm and the basic particle swarm optimization algorithm.

[0049] Attachment Figure 3 This is the pressure calculation result diagram of the example well. DETAILED DESCRIPTION

[0050] The present invention is not limited to the following embodiments, and specific implementation methods can be determined based on the technical solutions of the present invention and actual conditions.

[0051] The present invention will be further described below in conjunction with the embodiments:

[0052] Example 1: As shown in the attached Figure 1 As shown, the method for obtaining the pressure during the gas injection process of the injection and production well of the underground gas storage includes the following steps:

[0053] Step 1: Calculate the reservoir pressure of the underground gas storage during the gas injection process according to the reservoir pressure calculation method;

[0054] Step 2: Calculate the bottom hole pressure of the injection and production well during the gas injection process according to the bottom hole pressure calculation method;

[0055] Step 3: Calculate the wellhead oil pressure of the injection and production wells during the gas injection process according to the wellhead oil pressure calculation method;

[0056] Step 4: Calculate the objective function and evaluate the quality of the individual;

[0057] Step 5: Using the physical properties of the underground gas storage and field measured data, an improved particle swarm optimization algorithm is used to fit the objective function in the process of calculating the objective function to obtain the optimal value of the objective function, that is, the optimal values ​​of the reservoir pressure, bottom hole pressure, and wellhead oil pressure.

[0058] In step 1, the reservoir pressure calculation method is as follows:

[0059] The reservoir pressure calculation formula is:

[0060]

[0061] In formula (1), x = Kp0 / φμ;

[0062] Among them, p r is the reservoir pressure at the gas supply boundary, MPa; r is the gas well control radius, m; t is the gas injection time, d; p0 is the initial reservoir pressure, MPa; Q g is the gas injection rate, m 3 / s; μ is viscosity, Pa.s; K is permeability, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; p a is standard atmospheric pressure, Pa; is the natural gas compression factor under formation temperature and average formation pressure; T f is the formation temperature, K; T a is the standard temperature, K; -Ei() is the power integral function; φ is the porosity.

[0063] In step 2, the bottom hole pressure is calculated as follows:

[0064] The bottom hole pressure of the injection-production well is calculated using the production equation, and the formula is:

[0065]

[0066] Among them, p wf is the bottom hole flowing pressure, MPa; q g is the gas injection volume of the gas well, 10 4 m3 / d; A, B are the coefficients of the binomial production capacity equation, MPa 2 / (10 4 m 3 ).

[0067] In step 3, the wellhead oil pressure is calculated as follows:

[0068] The calculation method for the wellhead oil pressure of underground gas storage is based on the vertical pipe flow equation of gas flow in the wellbore. The calculation formula is:

[0069]

[0070]

[0071] Among them, P tf is the wellhead oil pressure, MPa; f is the wellbore friction coefficient; q g is the gas injection volume, m 3 / d; d is the inner diameter of the injection and production pipe, m; γ g is the relative density of gas; H is the depth from the wellhead to the middle of the gas layer, m; is the average temperature of the wellbore or well section, K; is the average compressibility factor of the wellbore or well section.

[0072] In step 4, the calculation formula of the objective function is:

[0073]

[0074] Among them, p tfi is the calculated wellhead oil pressure on the ith day, MPa; is the corresponding measured wellhead oil pressure, MPa; m is the total number of gas injection days.

[0075] In step 5, the step of improving the particle swarm optimization algorithm includes:

[0076] 1) Generate an initial group: randomly generate N individuals as the initial group,

[0077] X id =X imin +(X imax -X imin )·F1 (6)

[0078] Among them, X id represents the position of the dth dimension of the i-th individual; X imin represents the position of the minimum value of the dth dimension of the i-th individual; X imax represents the position of the maximum value of the d-th dimension of the i-th individual; F1 represents the function of generating random numbers in the interval (0,1);

[0079] 2) Calculate the objective function value: Substitute the generated initial population (permeability K, gas supply radius parameter r) as initial conditions into formula (1) to calculate the reservoir pressure of the underground gas storage, then calculate the bottom hole pressure of the injection and production well according to formula (2), and then substitute it into formula (3) to obtain the wellhead oil pressure of the injection and production well, and then calculate formula (5) to obtain the objective function value;

[0080] 3) Update speed and position formula: In the process of calculating the objective function, a strategy of automatically adjusting the inertia factor is introduced to adjust the global and local optimization performance, thereby achieving the effect of accelerating convergence and saving time.

[0081]

[0082] V id =ω·V id +2·F1·(P id -X id )+2·F1·(P gd -X id ) (8)

[0083] X id =X id +V id (9)

[0084] Among them, ω represents the automatic adjustment inertia factor, f i represents the objective function value of the i-th individual, f min represents the minimum value of the objective function, represents the average value of the objective function;

[0085] 4) Mutation operation: Introduce the mutation operation, randomly select the dth dimension of the i-th individual to mutate, and increase the diversity of the population;

[0086] X id =X id +F2 (10)

[0087] Among them, F2 represents a function that generates random numbers in the interval (-1,1);

[0088] Repeat steps 2) to 4) until the individual performance in the population meets the convergence requirements. At this time, the global optimal individual of the population is the optimal value of the objective function, that is, the optimal values ​​of reservoir pressure, bottom hole pressure, and wellhead oil pressure.

[0089] The convergence curves of the improved particle swarm optimization algorithm and the basic particle swarm optimization algorithm are shown in Figure 2a 、 Figure 2b .

[0090] In a certain underground gas storage, the reservoir pressure, bottom hole pressure, and wellhead oil pressure calculated by the method described in the embodiment are compared with the measured wellhead oil pressure. Figure 3 .

[0091] pass Figure 3 It can be seen that the calculated wellhead oil pressure has a high degree of fit with the measured wellhead oil pressure, indicating that the calculated wellhead oil pressure, reservoir pressure, and bottom hole pressure are close to their corresponding actual values.

[0092] The above technical features constitute the embodiments of the present invention, which have strong adaptability and implementation effect. Non-essential technical features can be added or removed according to actual needs to meet the requirements of different situations.

Claims

1. A method for obtaining the pressure during the gas injection process of an injection and production well of an underground gas storage reservoir, characterized in that The following steps are involved: Step 1: Calculate the reservoir pressure of the underground gas storage during the gas injection process according to the reservoir pressure calculation method; Step 2: Calculate the bottom hole pressure of the injection and production well during the gas injection process according to the bottom hole pressure calculation method; Step 3: Calculate the wellhead oil pressure of the injection and production wells during the gas injection process according to the wellhead oil pressure calculation method; Step 4: Calculate the objective function; Step 5: In the process of calculating the objective function, the improved particle swarm optimization algorithm is used to fit the calculation to obtain the optimal value of the objective function, that is, the optimal values ​​of the reservoir pressure, bottom hole pressure, and wellhead oil pressure; In step 1, the reservoir pressure is calculated as follows: The reservoir pressure calculation formula is: In formula (1), x = Kp0 / φμ; Among them, p r is the reservoir pressure at the gas supply boundary, MPa; r is the gas well control radius, m; t is the gas injection time, d; p0 is the initial reservoir pressure, MPa; Q g is the gas injection rate, m 3 / s; μ is viscosity, Pa.s; K is permeability, 10 -3 μm 2 ; h is the effective thickness of the reservoir, m; p a is standard atmospheric pressure, Pa; is the natural gas compression factor under formation temperature and average formation pressure; T f is the formation temperature, K; T a is the standard temperature, K; -Ei( ) is the power integral function; φ is the porosity; In step 2, the bottom hole pressure is calculated as follows: The bottom hole pressure of the injection-production well is calculated using the production equation, and the formula is: Among them, p wf is the bottom hole flowing pressure, MPa; q g is the gas injection volume of the gas well, 10 4 m 3 / d; A, B are the coefficients of the binomial production capacity equation, MPa 2 / (10 4 m 3 ); In step 3, the wellhead oil pressure is calculated as follows: The calculation method for the wellhead oil pressure of underground gas storage is based on the vertical pipe flow equation of gas flow in the wellbore. The calculation formula is: Among them, P tf is the wellhead oil pressure, MPa; f is the wellbore friction coefficient; q g is the gas injection volume, m 3 / d; d is the inner diameter of the injection and production pipe, m; γ g is the relative density of gas; H is the depth from the wellhead to the middle of the gas layer, m; is the average temperature of the wellbore or well section, K; is the average compressibility factor of the wellbore or well section; In step 4, the calculation formula of the objective function is: Among them, p tfi is the calculated wellhead oil pressure on the ith day, MPa; is the corresponding measured wellhead oil pressure, MPa; m is the total number of gas injection days.

2. The method for obtaining the pressure during the gas injection process of an injection-production well of an underground gas storage according to claim 1 is characterized in that In step five, the steps of improving the particle swarm optimization algorithm include: 1) Generate an initial group: randomly generate N individuals as the initial group, X id =X imin +(X imax -X imin )·F1 (6) Among them, X id represents the position of the dth dimension of the i-th individual; X imin represents the position of the minimum value of the dth dimension of the i-th individual; X imax represents the position of the maximum value of the d-th dimension of the i-th individual; F1 represents the function of generating random numbers in the interval (0,1); 2) Calculate the objective function value: Substitute the generated initial population as the initial condition into formula (1) to calculate the reservoir pressure of the underground gas storage, then calculate the bottom hole pressure of the injection and production well according to formula (2), and then substitute it into formula (3) to obtain the wellhead oil pressure of the injection and production well, and then calculate formula (5) to obtain the objective function value; 3) Update speed and position formula: In the process of calculating the objective function, a strategy of automatically adjusting the inertia factor is introduced to adjust the global and local optimization performance, thereby achieving the effect of accelerating convergence and saving time. V id =ω·V id +2·F1·(P id -X id )+2·F1·(P gd -X id ) (8) X id =X id +V id (9) Among them, ω represents the automatic adjustment inertia factor, f i represents the objective function value of the i-th individual, f min represents the minimum value of the objective function, represents the average value of the objective function; 4) Mutation operation: Introduce the mutation operation, randomly select the dth dimension of the i-th individual to mutate, and increase the diversity of the population; X id =X id +F2 (10) Among them, F2 represents a function that generates random numbers in the interval (-1,1); Repeat steps 2) to 4) until the individual performance in the population meets the convergence requirements. At this time, the global optimal individual of the population is the optimal value of the objective function, that is, the optimal values ​​of reservoir pressure, bottom hole pressure, and wellhead oil pressure.

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