A method for predicting pressure change rate in near-wellbore area depletion experiment of condensate gas reservoir

Abstract

The present invention relates to a method for predicting the pressure change rate of a depletion experiment in a near-wellbore area of ​​a condensate gas reservoir, comprising: S1. Assuming that the reservoir is a homogeneous porous medium, condensate oil and condensate gas are in radial seepage in the plane, and the original formation pressure before production is higher than the dew point pressure; S2. Obtaining the reservoir parameters, production parameters and fluid property parameters of the condensate gas reservoir; S3. Establishing a mathematical model for the seepage of condensate gas fluid; S4. Analytically solving the established mathematical model for the seepage to obtain a pressure distribution function at any position in the formation at any time; S5. Using the Euler method to derive the pressure change rate of any particle in the formation along the streamline direction; S6. Obtaining a specific expression for the pressure change rate of any particle in the condensate gas in the formation along the streamline direction; S7. Determining the pressure change rate value at any time and any position in the formation under different production conditions. The present invention can quickly and effectively predict the pressure change rate at any time in space, and more realistically simulate the non-equilibrium depletion process of the condensate gas reservoir.

Description

Technical Field

[0001] The invention belongs to the field of petroleum and natural gas development, and in particular relates to a method for predicting pressure change speed in a near-wellbore area depletion experiment of a condensate gas reservoir. Background Art

[0002] When the condensate gas reservoir fluid flows into the wellbore, the flow rate in the near-wellbore area increases rapidly due to the rapid drop in pressure. When the formation pressure is lower than the dew point pressure, the oil and gas phases are formed in the formation due to the retrograde condensation phenomenon. During the high-speed flow of the fluid in the near-wellbore area, the contact or separation time of the oil and gas phases is short, and the "condensation lag" phenomenon occurs, that is, a non-equilibrium phase change occurs. This is very different from the existing isothermal seepage model, which is based on the thermodynamic instantaneous equilibrium phase theory and predicts that the retrograde condensate oil saturation distribution in the near-wellbore area is significantly higher. In the near-wellbore area of ​​the condensate gas well, the pressure change speed is different at different locations and different time periods, resulting in large differences in the characteristics of the fluid phase change.

[0003] At present, many non-equilibrium phase change experiments in PVT cylinders and porous media have been carried out at home and abroad to study the influence of pressure change rate on condensate gas phase change and development effect. The experiment has obtained relatively consistent results: the pressure change rate is the main reason affecting the development of condensate gas reservoirs. In the process of fluid flowing from deep formation to production wells, the pressure does not drop uniformly. The closer to the production well, the faster the pressure change rate, and the more significant the non-equilibrium phenomenon. The production conditions of the production well are different, the pressure change rate is different at different locations, and even the pressure change rate is different at different production stages. However, during the indoor condensate gas depletion experiment, a constant pressure change rate was used for the experiment (Liu Nianqiu, Sun Lei, Zhou Jianfeng, et al. Research on the non-equilibrium phase state of constant volume depletion of volatile crude oil [J]. Journal of Chongqing University of Science and Technology (Natural Science Edition), 2015, 17(6): 23-26; Wei Dongchao, Li Yongjie, Yao Lin. Research on the non-equilibrium effect of high temperature and high pressure water-rich condensate gas system [J]. Journal of Chongqing University of Science and Technology (Natural Science Edition), 2013, 15(3); A non-equilibrium continuous depletion test method for condensate gas considering the influence of pressure reduction rate CN109917105A), which is quite different from the actual production situation.

[0004] It can be seen that due to the complex pressure depletion situation, serious retrograde condensation phenomenon, large differences in phase characteristics and significant non-equilibrium phenomenon in the near-wellbore area of ​​condensate gas reservoirs, the existing experimental equipment and methods are difficult to solve the above problems. It is urgent to establish a prediction method that can quickly and effectively determine the pressure change rate, so as to carry out non-equilibrium continuous depletion experiments with variable pressure change rate, and provide a theoretical basis and practical guidance for field production. Summary of the invention

[0005] The purpose of the present invention is to provide a method for predicting the pressure change rate in a near-wellbore area depletion experiment of a condensate gas reservoir. The method has reliable principles and is easy to operate. It can quickly and effectively predict the pressure change rate at any time in space. On this basis, a non-equilibrium continuous depletion experiment with a variable pressure change rate is carried out to more realistically simulate the non-equilibrium depletion process of a condensate gas reservoir, which is of great significance for studying the non-equilibrium phenomenon in the depletion development process of a condensate gas reservoir.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solutions.

[0007] A method for predicting pressure change rate in a near-wellbore area depletion experiment of a condensate gas reservoir comprises the following steps in sequence:

[0008] S1. Assume that the reservoir is a homogeneous porous medium, there is an operating well in an isothermal, isopause circular closed formation producing at a fixed rate, condensate oil and condensate gas flow radially in the plane, and the original formation pressure before production is higher than the dew point pressure;

[0009] S2. Obtain the reservoir parameters, production parameters and fluid property parameters of the condensate gas reservoir, such as porosity φ, permeability k, condensate gas viscosity μ g , condensate gas relative permeability k rg , gas reservoir thickness h, gas reservoir temperature T and gas well production q under standard surface conditions sc ;

[0010] S3. Establish a mathematical model for the seepage of condensate gas (the seepage equation refers to the national planning textbook for the "Eleventh Five-Year Plan" for general higher education: Li Xiaoping. Underground Oil and Gas Seepage Mechanics. Petroleum Industry Press, 2008, first edition):

[0011]

[0012] Where: p is the gas reservoir formation pressure, the pressure acting on the fluid in the rock pores, MPa; η is the pressure conductivity, μm 2 MPa / (mPa·s); μ g is the viscosity of condensate gas, mPa·s; φ is the porosity, %; C is the compressibility coefficient of condensate gas, MPa -1 ; k is permeability, μm 2 ;k rg is the relative permeability of condensate gas; t is the production time, h;

[0013] S4. Use mathematical physics methods to solve the established seepage mathematical model analytically and obtain the pressure distribution function at any position in the formation at any time:

[0014]

[0015] Where: r is the radius of any position, m; p e is the original formation pressure of the gas reservoir, MPa; q sc is the gas well production under standard surface conditions, 10 4 m 3 / d; Z is the condensate gas deviation factor; T is the gas reservoir temperature, K; h is the gas reservoir thickness, m; r e is the radius of the outer boundary of the gas reservoir, m;

[0016] S5. Considering the process of any particle of condensate gas in the condensate gas reservoir flowing along the streamline to the production well, the pressure change velocity dp / dt of any particle in the formation along the streamline direction is derived by using the Euler method (the spatial distribution function of the fluid motion described by the Euler method refers to the national planning textbook for general higher education in the "Eleventh Five-Year Plan": Yang Shuren. Engineering Fluid Mechanics. Petroleum Industry Press, 2006, first edition):

[0017]

[0018] Where: v g is the condensate gas seepage velocity, m / s; is the pressure change rate at a certain spatial position in the formation, MPa / h;

[0019] S6. Based on the pressure distribution function and the pressure change velocity of the particle along the streamline direction, the specific expression of the pressure change velocity of any particle of condensate gas in the formation along the streamline direction is obtained:

[0020]

[0021] S7. Determine the pressure change rate value at any time and any position in the formation under different production conditions.

[0022] Furthermore, the process of step S4 is as follows:

[0023] The initial conditions of the seepage differential equation are: p| t＝0 =p e

[0024] In a circular closed formation, the inner boundary well wall satisfies

[0025] Where: r w is the wellbore radius, m;

[0026] Satisfy at the outer boundary

[0027] The mathematical physics method is used to solve the analytical solution of the mathematical model, and the pressure distribution function (pressure square form) at any time and any position in the formation when the gas reservoir pressure wave disturbance completely spreads to the boundary is obtained:

[0028]

[0029] Furthermore, the process of step S5 is as follows:

[0030] According to the motion characteristics of fluid in space, the Euler method is used to describe the relationship between the pressure field p(x, y, z, t) in the condensate gas reservoir and the change in space and time. The pressure change speed of any particle along the streamline direction is:

[0031]

[0032] Where: u is the velocity of condensate gas in space, and its relationship with the seepage velocity in porous media is v g =φu;

[0033] Based on this, the pressure change rate of any particle of condensate gas in the formation is:

[0034]

[0035] Furthermore, the process of step S6 is as follows:

[0036] S61. Based on the obtained pressure distribution function and the composite function differential definition, the partial derivative of pressure with respect to distance is obtained as:

[0037]

[0038] S62. For the unsteady flow of condensate gas fluid, the partial derivative of the pressure at a certain position in the formation with respect to time is:

[0039]

[0040] S63. The specific expression of the pressure change rate of any particle of condensate gas in the formation is:

[0041]

[0042] Furthermore, the step S7 comprises:

[0043] S71. Simulate the production time t of the production well under different production allocation conditions, the formation pressure distribution at different positions in the condensate gas reservoir and the pressure change velocity curve of the near-well area under different production allocation conditions;

[0044] S72. Simulate different production times, and when the production allocation is q, the formation pressure distribution at different positions and different production times in the condensate gas reservoir and the pressure change rate curve of the near-wellbore area.

[0045] Furthermore, the pressure change rate in different pressure change intervals at a certain position is determined according to the pressure distribution and the pressure change rate curve, and a non-equilibrium continuous depletion experiment with variable pressure change rate is carried out (the non-equilibrium depletion experiment refers to the invention patent "A non-equilibrium continuous depletion test method for condensate gas considering the influence of pressure reduction rate" (CN2019101952796)).

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] The present invention can predict the pressure change rate of any particle of condensate gas in the formation at any position and at any time, and carry out non-equilibrium continuous depletion experiments with variable pressure change rates based on the pressure change rates predicted under different production conditions, thereby more realistically simulating the non-equilibrium depletion process of condensate gas reservoirs and providing guarantee for the efficient development of condensate gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 The present invention is a flow chart of a method for predicting the pressure change rate in a depletion experiment in the near-wellbore area of ​​a condensate gas reservoir.

[0049] Figure 2 This is the formation pressure distribution under different production allocation conditions after 100 days of production.

[0050] Figure 3 The distribution of pressure change rate in the near-wellbore area under different production allocation conditions after 100 days of production.

[0051] Figure 4 For the production of 10×10 4 m 3 Formation pressure distribution at different production times at 1:10 p.m. / d.

[0052] Figure 5 For the production of 10×10 4 m 3 Distribution of pressure change rate in the near-wellbore area at different production times at 10 / d. DETAILED DESCRIPTION

[0053] The present invention is further described below with reference to the accompanying drawings and examples, so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments, and for those skilled in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the attached claims, they are all protected.

[0054] Example

[0055] A method for predicting the pressure change rate of near-wellbore area depletion experiment in condensate gas reservoirs Figure 1 ), comprising the following steps in sequence:

[0056] S1. Assume that the condensate gas reservoir is a homogeneous porous medium, there is an operating well in an isothermal, isopause circular closed formation producing at a fixed production rate, condensate oil and gas seepage in radial plane, and the formation pressure before production is higher than the dew point pressure;

[0057] S2. Taking a condensate gas reservoir as an example, the reservoir parameters, production parameters and fluid property parameters of the condensate gas reservoir are obtained (the values ​​are shown in Table 1):

[0058] Table 1 Gas reservoir and fluid property parameters

[0059]

[0060] S3. According to the seepage characteristics of condensate gas, its seepage mathematical model is established, including: seepage differential equation, momentum equation, initial conditions and internal and external boundary conditions, and the unsteady seepage differential equation of condensate gas fluid is further simplified to:

[0061]

[0062] S4. Use mathematical physics methods to solve the established seepage mathematical model analytically and obtain the pressure distribution function;

[0063] The initial conditions of the seepage differential equation are: p| t＝0 =p e ; In a circular closed formation, the inner boundary well wall satisfies Satisfy at the outer boundary The mathematical physics method is used to solve the analytical solution of the mathematical model, and the pressure at the bottom of the well is obtained when the gas reservoir pressure wave disturbance completely reaches the boundary:

[0064]

[0065] S5. Considering the process of fluid flowing along the streamline in the condensate gas reservoir toward the well, the pressure change velocity dp / dt of any particle of condensate gas in the formation along the streamline direction is derived by the Euler method:

[0066]

[0067] S6. Based on the pressure distribution function and the pressure change velocity of the particle along the streamline direction, the specific expression of the pressure change velocity of any particle of condensate gas in the formation along the streamline direction is obtained:

[0068] S61. Based on the differential definition of the pressure distribution function and the composite function, the partial derivative of the pressure at the bottom of the well with respect to the position is obtained as follows:

[0069]

[0070] S62. For the unsteady flow of condensate gas, the partial derivative of the pressure at the bottom of the well with respect to time is:

[0071]

[0072] S63. The pressure change rate of any particle of condensate gas in the formation is:

[0073]

[0074] S7. Determine the pressure change rate value at any position and any time in the condensate gas reservoir under different production conditions:

[0075] S71. Figure 2 , Figure 3 As shown, the calculated allocation is 1×10 4 m 3 / d, 3×10 4 m 3 / d, 5×10 4 m 3 / d, 7×10 4 m 3 / d, 10×10 4 m 3 / d and 20×10 4 m 3 / d, the production well produces for 100 days, the pressure distribution at different positions in the condensate gas reservoir and the pressure change rate in the near-well area;

[0076] S72. Figure 4 , Figure 5 As shown in the figure, the production time of the production well is calculated to be 1 year, 5 years, 20 years, 30 years, 50 years, 60 years, 70 years and 75 years, and the production allocation is 10×10 4 m 3 / d, the pressure distribution at different positions in the condensate gas reservoir and the pressure change rate in the near-wellbore area.

[0077] Long cores were used to simulate the production situation within 1 m of the production well. The pressure in the core before the experiment was the original formation pressure of the gas reservoir, 41 MPa. Figure 4 , Figure 5 The average value of the pressure change rate corresponding to different pressure ranges at the bottom of the production well is read (see Table 2), and the non-equilibrium continuous depletion experiment of the porous medium long core is carried out according to the variable pressure change rate.

[0078] Table 2 Pressure change rate at different pressure ranges at bottom hole

[0079] Pressure range(MPa) Average pressure change rate (MPa / h) 41～35 5.8 35～30 7.9 30～25 13.6 25～20 19.5 20～15 34 Under 15 55

[0080] In summary, the present invention can effectively solve the problems faced by the non-equilibrium continuous depletion experiment with a constant pressure change rate indoor by predicting the pressure change rate of any particle of condensate gas in the formation at any position and at any time; the non-equilibrium continuous depletion experiment with a variable pressure change rate carried out in this way can more realistically simulate the non-equilibrium depletion process of condensate gas reservoirs.

Claims

1. A method for predicting the pressure change rate of a depletion experiment in a near-wellbore area of ​​a condensate gas reservoir, comprising the following steps in sequence: S1. Assume that the reservoir is a homogeneous porous medium, there is an operating well in an isothermal, isopause circular closed formation producing at a fixed rate, condensate oil and condensate gas flow radially in the plane, and the original formation pressure before production is higher than the dew point pressure; S2. Obtain reservoir parameters, production parameters and fluid property parameters of condensate gas reservoirs: porosity φ, permeability k, condensate gas viscosity μ g , condensate gas relative permeability k rg , gas reservoir thickness h, gas reservoir temperature T and gas well production q under standard surface conditions sc ; S3. Establish a mathematical model of condensate flow: Where: p is the gas reservoir formation pressure, the pressure acting on the fluid in the rock pores, MPa; η is the pressure conductivity coefficient, μm 2 MPa / (mPa·s); μ g is the viscosity of condensate gas, mPa·s; φ is the porosity, %; C is the compressibility coefficient of condensate gas, MPa -1 ; k is permeability, μm 2 ;k rg is the relative permeability of condensate gas; t is the production time, h; S4. Solve the established mathematical model of seepage analytically to obtain the pressure distribution function at any position in the formation at any time: Where: r is the radius of any position, m; p e is the original formation pressure of the gas reservoir, MPa; q sc is the gas well production under standard surface conditions, 10 4 m 3 / d; Z is the condensate gas deviation factor; T is the gas reservoir temperature, K; h is the gas reservoir thickness, m; r e is the radius of the outer boundary of the gas reservoir, m; S5. Use the Euler method to derive the pressure change velocity dp / dt of any particle in the formation along the streamline direction: Where: v g is the condensate gas seepage velocity, m / s; is the pressure change rate at a certain spatial position in the formation, MPa / h; S6. Obtain the specific expression of the pressure change velocity of any particle of condensate gas in the formation along the streamline direction: S7. Determine the pressure change rate value at any time and any position in the formation under different production conditions.

2. A method for predicting pressure change rate in near-wellbore area depletion experiment of condensate gas reservoir according to claim 1, characterized in that: The process of step S4 is as follows: The initial conditions of the seepage differential equation are: p| t＝0 =p e In a circular closed formation, the inner boundary well wall satisfies Where: r w is the wellbore radius, m; Satisfy at the outer boundary By solving the analytical solution of the mathematical model, we can obtain the pressure distribution function at any time and any position in the formation when the gas reservoir pressure wave disturbance completely reaches the boundary:

3. A method for predicting pressure change rate in near-wellbore area depletion experiment of condensate gas reservoir according to claim 1, characterized in that: The process of step S5 is as follows: According to the motion characteristics of fluid in space, the Euler method is used to describe the relationship between the pressure field p(x, y, z, t) in the condensate gas reservoir and the change in space and time. The pressure change speed of any particle along the streamline direction is: Where: u is the velocity of condensate gas in space, and its relationship with the seepage velocity in porous media is v g =φu; The pressure change rate of any particle of condensate gas in the formation is:

4. A method for predicting pressure change rate in near-wellbore area depletion experiment of condensate gas reservoir according to claim 1, characterized in that: The process of step S6 is as follows: S61. Based on the obtained pressure distribution function and the composite function differential definition, the partial derivative of pressure with respect to distance is obtained as: S62. For the unsteady flow of condensate gas fluid, the partial derivative of the pressure at a certain position in the formation with respect to time is: S63. The specific expression of the pressure change rate of any particle of condensate gas in the formation is:

5. The method for predicting the pressure change rate of the near-wellbore area depletion experiment in a condensate gas reservoir according to claim 1, characterized in that: The step S7 comprises: S71. Simulate the production time t of the production well under different production allocation conditions, the formation pressure distribution at different positions in the condensate gas reservoir and the pressure change velocity curve of the near-well area under different production allocation conditions; S72. Simulate different production times, and when the production allocation is q, the formation pressure distribution at different positions and different production times in the condensate gas reservoir and the pressure change rate curve of the near-wellbore area.

6. A method for predicting pressure change rate in near-wellbore area depletion experiment of condensate gas reservoir according to claim 5, characterized in that: The pressure change rate in different pressure change intervals at a certain location is determined based on the pressure distribution and the pressure change rate curve, and a non-equilibrium continuous depletion experiment with variable pressure change rate is carried out.

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