Gas drive pressure quantitative calculation method for gas-water relative permeability experiment by unsteady-state method

Abstract

The invention discloses a gas drive pressure quantitative calculation method for an unsteady-state method gas-water relative permeability experiment. Comprising the following steps: S1, acquiring basic data; s2, testing the gas permeability Kg under a plurality of pressure points, and calculating the Kirschner permeability K infinity; s3, normalizing the relative permeability curve to obtain the gas phase relative permeability # imgabs0 # under the irreducible water condition; S4, calculating the upper limit value P30 and the lower limit value P7 of the gas drive pressure; and S5, the gas drive pressure median value Pg is calculated. The gas displacement pressure range calculation method has the beneficial effects that the gas displacement pressure range is calculated according to the core tail end outlet gas flow range, the core length, the diameter, the Kirschner permeability, the atmospheric pressure, the gas viscosity and the reservoir relative permeability given by the standard, and the operation is more convenient.

Description

Technical Field

[0001] The invention relates to the technical field of petrochemical industry, and in particular to a method for quantitatively calculating gas drive pressure in a non-steady-state gas-water phase permeability experiment. Background Art

[0002] The relative permeability curve is an important parameter for the development and evaluation of oil and gas reservoirs, and is of great significance for understanding the seepage law of oil and gas reservoirs. The non-steady-state method is a relative permeability determination method commonly used in laboratories in the industry. The experimental test requires high equipment measurement accuracy, and the displacement conditions are often determined by empirical methods. For tight reservoirs, the sample pore volume is small, the fluid volume is small, the pore throat is narrow, and the fluidity is poor, which requires higher equipment measurement accuracy and data stability. In the industry, the gas drive pressure selection for the gas-water relative permeability experiment of tight gas reservoirs generally adopts empirical values, resulting in large or small terminal fluid flow rates, which cannot meet the technical parameters of the standard GB / T 28912-2012 "Method for Determination of Relative Permeability of Two-Phase Fluids in Rocks", which requires that the gas drive water production rate be between 7mL / min and 30mL / min, thus affecting the experimental accuracy and quality control. Therefore, the proposed method for quantitative calculation of gas drive pressure in the non-steady-state gas-water relative permeability experiment will inevitably serve as an important technical method for determining experimental conditions, especially for the gas drive water production rate required by the stability standard. Under the existing technology, the empirical method used to determine the gas drive pressure in the non-steady-state gas-water relative permeability experiment cannot provide quantitative gas drive pressure and stable gas drive water production rate. Summary of the invention

[0003] The object of the present invention is to provide a method for quantitatively calculating gas displacement pressure in a non-steady-state gas-water relative permeability experiment, which calculates the gas displacement pressure range through the standard given core end outlet gas flow range, core length, diameter, Kerber permeability, atmospheric pressure, gas viscosity, and reservoir relative permeability, and is more convenient to operate.

[0004] To achieve the above object, the present invention adopts the following technical solution, including the following steps:

[0005] S1. Collect basic data;

[0006] S2. Test the gas permeability K at multiple pressure points g , and calculate the Kirkpatrick permeability K ∞ ;

[0007] S3. Normalize the relative permeability curve to obtain the gas phase relative permeability under bound water conditions

[0008] S4. Calculate the upper limit of gas drive pressure P 30 , lower limit value P7;

[0009] S5. Calculate the median gas drive pressure Pg .

[0010] Preferably, in step S1, the basic data include core length, core diameter, and environmental parameters such as atmospheric pressure and temperature.

[0011] Preferably, in step S2, the K-rated permeability K ∞ The calculation formula is:

[0012]

[0013] Among them, P m is the average pore pressure, MPa; P1 and P2 are the absolute pressures of the gas at the inlet and outlet of the core, MPa; P a is atmospheric pressure, MPa; Q is the gas flow rate at the outlet, cm 3 / s; μ is gas viscosity, mPa·s; L is rock sample length, cm; A is rock sample cross-sectional area, cm 2 ; K g is the gas permeability, mD; b is the gas slip coefficient; K ∞ is the Klein permeability, mD.

[0014] Preferably, in step S3, the relative permeability of the gas phase under the condition of bound water is The method is: according to the characteristics of the gas reservoir, select representative relative permeability curves of water and gas, and calculate the standard relative permeability curve data of the basic curve according to the selected relative permeability curve:

[0015]

[0016] Normalized phase permeability definition:

[0017]

[0018] Perform logarithmic conversion on the above two formulas:

[0019]

[0020] Through linear regression, the values ​​of m and n are calculated respectively, and then the geometric mean of m and n is calculated. The values ​​of m and n are substituted into the definition formula of standardized relative permeability to calculate the standardized relative permeability. Then find K rw , K rg , S w ;

[0021]

[0022] in, is the standardized relative permeability of water and gas, decimal; K rw , Krg is the relative permeability of water and gas, decimal; is the relative permeability of water under residual gas conditions, decimal; S is the relative permeability of the gas phase under bound water conditions, a decimal; w , S wi , S gr are water saturation, irreducible water saturation, and residual gas saturation, respectively, in decimals; is the standardized water saturation, decimal; m , n is a constant;

[0023] According to the above calculation, the relative permeability of the gas phase under the condition of bound water after the overall normalization of the relative permeability curve can be obtained:

[0024]

[0025] Preferably, in step S4, the upper limit value of the gas drive pressure P 30 、Calculation method of lower limit value P7:

[0026] The gas drive production rate is between 7mL / min and 30mL / min. Assuming that the gas flow in a short period of time conforms to Darcy's law and the flowing fluid is mainly gas, the gas drive pressure under 7mL / min and 30mL / min conditions can be calculated. The calculation formula is as follows;

[0027]

[0028] Among them, P a is atmospheric pressure, MPa; Q MAX is the maximum flow rate, mL / min; Q MIN is the minimum flow rate, mL / min; μ is the gas viscosity, mPa·s; L is the core length, cm; A is the core cross-sectional area, cm 2 ; K is the relative permeability of the gas phase under bound water conditions after normalization of the relative permeability curve, decimal; ∞ is the Kirkpatrick permeability, mD; P 30 P is the upper limit of gas drive pressure, MPa; P7 is the lower limit of gas drive pressure, MPa.

[0029] Preferably, in step S5, the gas drive pressure median P g The calculation formula is:

[0030]

[0031] Among them, P 30 is the upper limit of gas drive pressure, MPa; P7 is the lower limit of gas drive pressure.

[0032] The beneficial effects of the present invention are as follows: the gas displacement pressure range is calculated by using the standard given core end outlet gas flow range, core length, diameter, Kerber permeability, atmospheric pressure, gas viscosity, and reservoir relative permeability, which makes the operation more convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic flow chart of the quantitative calculation method of the gas drive pressure in the non-steady-state gas-water relative permeability experiment of the present invention.

[0034] Figure 2 is the gas permeability K in Example 1 of the present invention g The reciprocal of the average absolute pressure of upstream and downstream 1 / P m Relationship diagram.

[0035] Figure 3 It is the standardized gas-water relative permeability curve in Example 1 of the present invention.

[0036] Figure 4 It is the normalized gas-water relative permeability curve of sample No. 1 in Example 1 of the present invention.

[0037] Figure 5 It is the normalized gas-water relative permeability curve of sample No. 2 in Example 1 of the present invention.

[0038] Figure 6 It is the normalized gas-water relative permeability curve of sample No. 3 in Example 1 of the present invention.

[0039] Figure 7 It is the normalized gas-water relative permeability curve of sample No. 4 in Example 1 of the present invention.

[0040] Figure 8 It is the normalized gas-water relative permeability curve of sample No. 5 in Example 1 of the present invention.

[0041] Fig. 9 It is the normalized gas-water relative permeability curve of sample No. 6 in Example 1 of the present invention.

[0042] Fig.10 It is the overall normalized gas-water relative permeability curve in Example 1 of the present invention. DETAILED DESCRIPTION

[0043] The invention is further described in detail below in conjunction with the accompanying drawings so that those skilled in the art can implement it according to the description.

[0044] It should be understood that terms such as “having”, “including” and “comprising” used herein do not exclude the existence or addition of one or other elements or combinations thereof.

[0045] like Figure 1-10As shown, a method for quantitatively calculating gas drive pressure in a non-steady-state gas-water relative permeability experiment of the present invention comprises the following steps:

[0046] S1. Collect basic data;

[0047] The basic data include a length of 3.496 cm, a diameter of 2.522 cm, environmental parameters of atmospheric pressure of 0.103 MPa and a temperature of 17°C.

[0048] S2. Test the gas permeability K at 5 pressure points g , and calculate the Kirkpatrick permeability K ∞ ;

[0049] The K-value permeability K ∞ The calculation formula is:

[0050]

[0051]

[0052] Among them, P m is the average pore pressure, MPa; P1 and P2 are the absolute pressures of the gas at the inlet and outlet of the core, MPa; P a is atmospheric pressure, MPa; Q is the gas flow rate at the outlet, cm 3 / s; μ is gas viscosity, mPa·s; L is rock sample length, cm; A is rock sample cross-sectional area, cm 2 ; K g is the gas permeability, mD; b is the gas slip coefficient; K ∞ is the Klein permeability, mD.

[0053] The atmospheric pressure is 0.103MPa, the pressure P2 at the core outlet is 0.103MPa, and the pressure P1 at the core inlet is continuously measured. Five pressures are 0.172MPa, 0.240MPa, 0.310MPa, 0.379MPa, and 0.447MPa, respectively. The corresponding average absolute pressures at both ends of the core are 0.137MPa, 0.171MPa, 0.206MPa, 0.241MPa, and 0.275MPa, respectively. The gas permeabilities under the corresponding pressures are measured to be 0.423mD, 0.352mD, 0.323mD, 0.308mD, and 0.286mD, respectively.

[0054] The gas permeability K g is the dependent variable, 1 / P m Fit a linear equation to the independent variable, such as Figure 2 As shown, the equation is as follows:

[0055] K g =0.0362 / Pm +0.152

[0056] The intercept obtained is the Kirkpatrick permeability K ∞ , that is, 0.152mD, and the gas slip coefficient b is 0.238MPa. The relationship between gas permeability and the inverse of the average value of the upstream and downstream absolute pressures is shown in the figure below: Figure 2 .

[0057] S3. Normalize the relative permeability curve to obtain the gas phase relative permeability under bound water conditions Gas phase relative permeability under bound water conditions The method is: select 6 groups of representative relative permeability curves of water and gas, and calculate the standard relative permeability curve data of the basic curve according to the selected relative permeability curves:

[0058]

[0059]

[0060] The calculation data and results are detailed in the table below.

[0061] Table 1 Single sample basic experimental data and calculation results of standard phase permeability curve data

[0062]

[0063]

[0064] Normalized phase permeability definition:

[0065]

[0066] Perform logarithmic conversion on the above two formulas:

[0067]

[0068] Through linear regression, the values ​​of m and n are calculated respectively, and then the geometric mean of m and n is calculated.

[0069] After regression and calculation of the 6 sets of data, the geometric mean of m is 1.0610 and the geometric mean of n is 1.4201, as shown in the table below.

[0070] Table 2 Calculation results of m and n values

[0071]

[0072]

[0073] Substitute the values ​​of m and n into the definition formula of standardized relative permeability to obtain the standardized relative permeability The calculation results are shown in the following table, and the standardized gas-water relative permeability curve is drawn as follows: Figure 3 ;

[0074] Then find K rw , K rg , S w ;

[0075]

[0076] in, is the standardized relative permeability of water and gas, decimal; K rw , K rg is the relative permeability of water and gas, decimal; is the relative permeability of water under residual gas conditions, decimal; S is the relative permeability of the gas phase under bound water conditions, a decimal; w , S wi , S gr are water saturation, irreducible water saturation, and residual gas saturation, respectively, in decimals; is the standardized water saturation, a decimal; m and n are constants; the normalized gas-water relative permeability curve of each single sample is obtained as follows Figure 3 , Figure 4 one Fig. 9 , the calculation data results are shown in Table 3;

[0077] Table 3 Calculation results of single sample standardization and normalized phase permeability curve

[0078]

[0079]

[0080] The S of 6 groups of samples wi , S gr , The arithmetic mean is the basic value, The values ​​were assigned from 0 to 1 with an interval of 0.1, and the six groups of samples were standardized according to the equation and the equal distribution. calculate standardization

[0081]

[0082] Then find K rw , K rg , S w ;

[0083]

[0084] The calculation results are shown in Table 4, and the normalized phase permeability curves of the six groups of samples are obtained as follows: Fig.10 Shown

[0085] Table 4 Calculation results of overall normalized phase permeability curve

[0086]

[0087] According to the above calculation, the gas phase relative permeability under the condition of bound water after the normalization of the relative permeability curve can be obtained:

[0088]

[0089] in, K is the relative permeability of the gas phase under the condition of bound water in the standardized gas-water relative permeability curve, which is taken as 1. rg The arithmetic mean of the relative permeability of the gas phase under the condition of bound water of different samples in a certain formation is 0.323. It is 0.323.

[0090] S4. Calculate the upper limit of gas drive pressure P 30 , lower limit value P7;

[0091] Gas drive pressure upper limit P 30 、Calculation method of lower limit value P7:

[0092] The gas drive production rate is between 7mL / min and 30mL / min. Assuming that the gas flow in a short period of time conforms to Darcy's law and the flowing fluid is mainly gas, the gas drive pressure under 7mL / min and 30mL / min conditions can be calculated. The calculation formula is as follows;

[0093]

[0094] Among them, P a is atmospheric pressure, MPa; Q MAX is the maximum flow rate, mL / min; Q MIN is the minimum flow rate, mL / min; μ is the gas viscosity, mpa·s; L is the core length, cm; A is the core cross-sectional area, cm 2 ; K is the relative permeability of the gas phase under bound water conditions after normalization of the relative permeability curve, decimal; ∞ is the Kirkpatrick permeability, mD; P 30 P is the upper limit of gas drive pressure, MPa; P7 is the lower limit of gas drive pressure, MPa.

[0095] P a 0.103MPa; Q MAX 30mL / min; Q MINis 7mL / min; μ is 0.0176mPa·s; L is 3.496cm; A is 4.996cm 2 ; is 0.323; K ∞ It is 0.152mD.

[0096]

[0097] The upper limit of gas drive pressure P is calculated. 30 1.508MPa, lower limit value P7 is 0.680MPa

[0098] S5. Calculate the median gas drive pressure P g .

[0099] The gas drive pressure median P g The calculation formula is:

[0100]

[0101] Among them, P 30 P7 is the upper limit of gas drive pressure, 1.508MPa, and P7 is the lower limit of gas drive pressure, 0.680MPa.

[0102]

[0103] The median gas drive pressure P is calculated g It is 1.094MPa.

[0104] In summary, the quantitative calculation method of gas displacement pressure in the non-steady-state gas-water relative permeability experiment of the present invention calculates the gas displacement pressure range through the standard given core end outlet gas flow range, core length, diameter, Kolmar permeability, atmospheric pressure, gas viscosity, reservoir relative permeability, and is more convenient to operate.

[0105] Although the embodiments of the present invention have been disclosed as above, they are not limited to the applications listed in the specification and the implementation modes, and they can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for quantitatively calculating gas displacement pressure in a non-steady-state gas-water relative permeability experiment, characterized in that: The following steps are involved: S1. Collect basic data; S2. Test the gas permeability K at multiple pressure points g , and calculate the Kirkpatrick permeability K ∞ ; S3. Normalize the relative permeability curve to obtain the gas phase relative permeability under bound water conditions S4. Calculate the upper limit of gas drive pressure P 30 , lower limit value P7; S5. Calculate the median gas drive pressure P g .

2. The method for quantitatively calculating gas displacement pressure in the non-steady-state gas-water relative permeability experiment according to claim 1 is characterized in that: In step S1, the basic data include core length, core diameter, and environmental parameters such as atmospheric pressure and temperature.

3. The method for quantitatively calculating gas displacement pressure in the non-steady-state gas-water relative permeability experiment according to claim 2 is characterized in that: In step S2, the K-value K ∞ The calculation formula is: Among them, P m is the average pore pressure, MPa; P1 and P2 are the absolute pressures of the gas at the inlet and outlet of the core, MPa; P a is atmospheric pressure, MPa; Q is the gas flow rate at the outlet, cm 3 / s; μ is gas viscosity, mPa·s; L is rock sample length, cm; A is rock sample cross-sectional area, cm 2 ; K g is the gas permeability, mD; b is the gas slip coefficient; K ∞ is the Klein permeability, mD.

4. The method for quantitatively calculating gas displacement pressure in the non-steady-state gas-water relative permeability experiment according to claim 3 is characterized in that: In step S3, the relative permeability of the gas phase under the condition of bound water is The method is: according to the characteristics of the gas reservoir, select representative relative permeability curves of water and gas, and calculate the standard relative permeability curve data of the basic curve according to the selected relative permeability curve: Normalized phase permeability definition: Perform logarithmic conversion on the above two formulas: Through linear regression, the values ​​of m and n are calculated respectively, and then the geometric mean of m and n is calculated. The values ​​of m and n are substituted into the definition formula of standardized relative permeability to calculate the standardized relative permeability. Then find K rw , K rg , S w ; in, is the standardized relative permeability of water and gas, decimal; K rw , K rg is the relative permeability of water and gas, decimal; is the relative permeability of water under residual gas conditions, decimal; S is the relative permeability of the gas phase under bound water conditions, a decimal; w , S wi , S gr are water saturation, irreducible water saturation, and residual gas saturation, respectively, in decimals; is the standardized water saturation, a decimal; m and n are constants; According to the above calculation, the relative permeability of the gas phase under the condition of bound water after the overall normalization of the relative permeability curve can be obtained: 。 5. The method for quantitatively calculating gas displacement pressure in the non-steady-state gas-water relative permeability experiment according to claim 4 is characterized in that: In step S4, the upper limit value of the gas drive pressure P 30 、Calculation method of lower limit value P7: The gas drive production rate is between 7mL / min and 30mL / min. Assuming that the gas flow in a short period of time conforms to Darcy's law and the flowing fluid is mainly gas, the gas drive pressure under 7mL / min and 30mL / min conditions can be calculated. The calculation formula is as follows; Among them, P a is atmospheric pressure, MPa; Q MAX is the maximum flow rate, mL / min; Q MIN is the minimum flow rate, mL / min; μ is the gas viscosity, mPa·s; L is the core length, cm; A is the core cross-sectional area, cm 2 ; K is the relative permeability of the gas phase under bound water conditions after normalization of the relative permeability curve, decimal; ∞ is the Kirkpatrick permeability, mD; P 30 is the upper limit of gas drive pressure, MPa; P7 is the lower limit of gas drive pressure, MPa.

6. The method for quantitatively calculating gas displacement pressure in the non-steady-state gas-water relative permeability experiment according to claim 5 is characterized in that: In step S5, the gas drive pressure median P g The calculation formula is: Among them, P 30 is the upper limit of gas drive pressure, MPa; P7 is the lower limit of gas drive pressure.

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