A calculation method of production splitting coefficient based on isothermal compressibility

Abstract

The present invention relates to the technical field of oil and gas field development, and specifically relates to a method for calculating the production splitting coefficient based on the isothermal compressibility coefficient. The production splitting coefficients of each producing layer are calculated using the formula. The present invention clarifies the determining factors of the production splitting coefficient, proposes a simple calculation procedure, enriches the calculation methods of the production splitting coefficient, and has guiding significance for gas reservoir development.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas field development, and particularly relates to a method for calculating production splitting coefficient based on isothermal compressibility coefficient. Background Art

[0002] The production splitting coefficient is the core parameter of a multi-layer commingled production gas well, which directly determines the accuracy of dynamic analysis. From the perspective of acquisition methods, the production splitting coefficient includes the testing method and the calculation method. The testing method includes methods such as gas production profile testing and physical model experiments. However, the testing method is time-consuming and costly, resulting in limited on-site application. In the gas field, the calculation method is mainly used.

[0003] The production splitting coefficient is affected by the combined action of reservoir seepage and wellbore pipe flow, and there are many influencing parameters. According to different calculation principles and parameters used, the calculation method can be divided into the static parameter method, numerical simulation, wellbore pressure gradient method, seepage mechanics method, etc. Among them: the static parameter method has a large error; the numerical simulation method is time-consuming; the wellbore pressure gradient method requires accurate acquisition of data such as bottom-hole flowing pressure and temperature of each production layer; the seepage mechanics method needs to be solved by means of multiple loops such as recursion and iteration. Different calculation methods have different requirements for parameters. Due to the differences in the parameters of gas wells, some gas wells cannot be calculated using the current methods. Establishing a method for calculating production splitting coefficient based on isothermal compressibility coefficient is a supplement and improvement to the calculation method of production splitting coefficient, and has guiding significance for gas reservoir development. Summary of the Invention

[0004] The present invention aims to address the above problems and proposes a method for calculating production splitting coefficient based on isothermal compressibility coefficient.

[0005] The technical solution of the present invention lies in:

[0006] A method for calculating production splitting coefficient based on isothermal compressibility coefficient is as follows:

[0007] According to the physical and chemical properties of natural gas, the isothermal compressibility coefficient of natural gas is:

[0008]

[0009] In the formula: C gj is the isothermal compressibility coefficient of natural gas in production layer j, MPa -1 ;

[0010] V j is the volume of natural gas in production layer j, m 3 ;

[0011] is the average formation pressure of production layer j, MPa;

[0012] Separate variables in equation (1), take the derivative with respect to time, and obtain:

[0013]

[0014] Where: t is the production time, d;

[0015] q gj is the underground gas production of pay zone j, m 3 / d;

[0016] For a constant-volume gas reservoir, the natural gas volume of pay zone j is written as:

[0017] V j = π(r ej 2 -r w 2 )h j φ j S gj (3)

[0018] Where: r ej is the control radius of pay zone j, m;

[0019] r w is the wellbore radius, m;

[0020] h j is the thickness of pay zone j, m;

[0021] is the porosity of pay zone j, dimensionless;

[0022] S gj is the gas saturation of pay zone j, dimensionless.

[0023] Substitute equation (3) into equation (2), separate variables, and integrate to derive:

[0024]

[0025] The definition of the volume coefficient is:

[0026]

[0027] Where: B gj is the volume coefficient of pay zone j, dimensionless;

[0028] q scj is the surface gas production of pay zone j, m 3 / d;

[0029] Z rj is the corresponding deviation factor, dimensionless;

[0030] Tj is the temperature of the production layer j, K;

[0031] p sc is standard pressure, MPa;

[0032] T sc is standard temperature, K;

[0033] Substituting equation (5) into equation (4), we get the expression of surface gas production:

[0034]

[0035] In addition, the yield splitting coefficient is defined as:

[0036]

[0037] Where: j is the production splitting coefficient of production layer j, dimensionless;

[0038] n is the number of producing layers, dimensionless;

[0039] Substituting formula (6) into formula (7), we can obtain the theoretical formula of the production splitting coefficient:

[0040]

[0041] (8) where the isothermal compressibility coefficient of natural gas in production layer j is C gj , coefficient of deviation Z rj is the average formation pressure Function, and contains The derivative of Represents the formation pressure term, MPa / d.

[0042] According to formula (8), the production splitting coefficient ◇ j It consists of 3 items: Reservoir parameter item Control radius term r ej 2 -r w 2 and formation pressure Substituting these three items, we can get the production splitting coefficient◇ j ; But the difficulty lies in calculating the formation pressure term According to the material balance principle, the formation pressure term is a fixed value, due to The value of depends on the production split coefficient◇ j , which makes it impossible to solve them jointly, so an approximate method is needed.

[0043] On the one hand, according to the principles of gas reservoir engineering, the average formation pressure during the production of a fixed-yield gas well is It shows a linear change with the production time t, and the fitting relationship is expressed as:

[0044]

[0045] In the formula: a rj is the slope of the linear fitting relationship between and t, a constant;

[0046] b rj is the intercept of the linear fitting relationship between and t, a constant;

[0047] Deriving equation (9) with respect to the time t, we get:

[0048]

[0049] On the other hand, the experimental data of the high-pressure physical properties of natural gas show that changes little with and can be approximated as a constant value; since has been determined to be a constant according to equation (10), combined with the formation pressure term being a constant value, for the convenience of calculation, taking and substituting it together with equation (10), we get the calculation formula for the formation pressure term :

[0050]

[0051] In the formula: C gij is the original isothermal compressibility coefficient of natural gas in pay zone j, MPa -1 ;

[0052] p ij is the original formation pressure in pay zone j, MPa;

[0053] Z rij is the original deviation factor in pay zone j, dimensionless.

[0054] The technical effect of the present invention is that:

[0055] The present invention establishes a calculation method for the production splitting coefficient based on the isothermal compressibility coefficient, clarifies the determining factors of the production splitting coefficient, proposes a simple calculation step, enriches the calculation method of the production splitting coefficient, and has guiding significance for gas reservoir development. Description of the Drawings

[0056] Figure 1 It is a graph of the change curve of the average formation pressure of each pay zone with the production time t and the linear fitting relationship in a specific experimental example. Detailed Embodiments

[0057] A method for calculating the production splitting coefficient based on the isothermal compressibility coefficient is as follows:

[0058] Step 1: Calculate the formation pressure term through formula (11);

[0059]

[0060] Step 2: Calculate the production splitting coefficient of each production layer through formula (8). j ;

[0061]

[0062] Specific experimental example - Using a numerical simulation well for the implementation of the calculation method of the present invention and the verification of the calculation results. The number of production layers of the numerical simulation well in this example is 4, and it produces at a constant production rate of 50000 m 3 / d. The variation curve of the average formation pressure of each production layer with the production time t and the linear fitting relationship are shown in ; Figure 1 .

[0063] The numerical simulation results show that the production rates and production splitting coefficients of each production layer are respectively:

[0064] When j = 1, the average q scj = 6287.16 m 3 / d, and the◇ j of the numerical simulation is 12.57%;

[0065] When j = 2, the average q scj = 5662.36 m 3 / d, and the◇ j of the numerical simulation is 11.33%;

[0066] When j = 3, the average q scj = 1760.51 m 3 / d, and the◇ j of the numerical simulation is 3.52%;

[0067] When j = 4, the average q scj = 36289.97 m 3 / d, and the◇ j of the numerical simulation is 72.58%;

[0068] The production splitting coefficient obtained through numerical simulation is regarded as the true value.

[0069] Calculate the production splitting coefficient of each production layer through the production splitting coefficient calculation method based on the isothermal compressibility coefficient provided by the present invention◇ j ; The specific method is as follows:

[0070] The parameters of each pay zone are shown in Table 1.

[0071] Table 1 Calculation Parameters of Production Split Coefficient

[0072]

[0073] Step 1: Calculate the formation pressure term

[0074] The formation pressure terms of each pay zone are calculated using Equation (11).

[0075] When j = 1,

[0076] When j = 2,

[0077] When j = 3,

[0078] When j = 4,

[0079] Step 2: Calculate the production split coefficient ◇ j ;

[0080] The production split coefficients of each pay zone are calculated using Equation (8). ◇ j ;

[0081] When j = 1, for the present invention ◇ j = 12.59%;

[0082] When j = 2, for the present invention ◇ j = 11.77%;

[0083] When j = 3, for the present invention ◇ j = 3.48%;

[0084] When j = 4, for the present invention ◇ j = 72.16%.

[0085] The production split coefficients calculated by the present invention are compared with those obtained by numerical simulation. The comparison results are shown in Table 2. It can be seen from Table 2 that the absolute value of the relative error between the calculated value and the true value of the production split coefficient obtained by the method provided by the present invention ranges from 0.16% to 3.88%, and the average error is 1.44%; indicating that the present invention has high accuracy.

[0086] Table 2 Comparison of Calculation Results of Production Split Coefficient

[0087] pay zone the present invention numerical simulation absolute value of relative error pay zone 1 12.59％ 12.57％ 0.16％ pay zone 2 11.77％ 11.33％ 3.88％ pay zone 3 3.48％ 3.52％ 1.14％ pay zone 4 72.16％ 72.58％ 0.58％ .

Claims

1. A method for calculating the production splitting coefficient based on the isothermal compressibility coefficient, characterized in that: the method is as follows: In the formula: is the production splitting coefficient of pay zone j, dimensionless; h j is the thickness of pay zone j, m; is the porosity of pay zone j, dimensionless; S gj Gas saturation of pay zone j, dimensionless; T j is the temperature of pay zone j, K; r ej is the control radius of pay zone j, m; r w is the wellbore radius, m; C gj Isothermal compressibility of natural gas for pay zone j, MPa -1 ; is the average formation pressure of pay zone j, MPa; Z rj is the corresponding deviation coefficient, dimensionless; t is the production time, d; is the formation pressure term, MPa / d; n is the number of production layers, dimensionless.

2. The method for calculating the production splitting coefficient based on the isothermal compressibility coefficient according to claim 1, characterized in that: the specific calculation process of the formation pressure term is: where: C gij is the original isothermal compressibility of natural gas in pay zone j, MPa -1 ; p ij Original formation pressure of pay zone j, MPa; Z rij is the original deviation coefficient of pay zone j, dimensionless; a rj for pay zone j and the slope and constant of the linear fitting relationship with t

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