Determination method of porosity and permeability of unconventional core under different net confining pressure and its application

Abstract

The application discloses a method for determining porosity and permeability of unconventional cores under different net confining pressures and application thereof, and the method comprises the following steps: obtaining the porosity and permeability of the core under initial pressure through core analysis; calculating the T2 geometric mean value by using the nuclear magnetic resonance T2 spectrum data under different net pressures; and finally, combining the mathematical model proposed in the application, and then calculating the porosity and permeability of the core under different net confining pressures. The method does not need to repeatedly correct parameters, overcomes the problem of complicated parameter determination in the traditional nuclear magnetic resonance classical porosity and permeability model, and can realize the rapid measurement of the porosity and permeability of the core under different stress states, and has good effects on dense sandstone and shale samples.

Description

Technical Field

[0001] This invention relates to a method for determining porosity and permeability, and particularly to a method for determining porosity and permeability under different net confining pressures in unconventional core samples and its application. Background Technology

[0002] my country possesses abundant unconventional oil and gas resources, and a deep understanding and efficient development of these resources is a hot research topic for scholars both domestically and internationally. Unconventional reservoirs, due to their poor physical properties—typically low-porosity, low-permeability rocks—face significant challenges in oil and gas flow, making their development more difficult than that of conventional reservoirs. Furthermore, as fluids are extracted from the pores, the effective stress on the reservoir increases, leading to pore compression and a decrease in porosity and permeability. These stress and porosity / permeability changes become even more complex during energy replenishment or CO2 huff and puff to enhance recovery. Determining the changes in porosity and permeability is fundamental to reservoir evaluation and a key issue in the field of oil and gas development.

[0003] Currently, unconventional core porosity and permeability testing under varying effective stress conditions includes direct methods and conventional nuclear magnetic resonance (NMR) methods. Direct methods measure core porosity and permeability directly through steady-state or unsteady-state overburden pressure porosity and permeability. Conventional NMR technology can measure both porosity and permeability. Porosity measurement primarily involves calibration using standard calibrated samples. By establishing a relationship between hydrogen nuclei and total magnetization, and measuring the NMR signal of water-saturated rock samples under the same parameters, the ratio of the signal intensity of the sample to that of the standard sample represents the porosity ratio, thus allowing the determination of the rock sample's porosity. Permeability measurement mainly utilizes the SDR and Timur / Coates models: the SDR model simply averages the pore size distribution, using the geometric mean of the T² distribution to estimate permeability; the Timur / Coates model uses porosity, bound water saturation, and the free fluid index to predict permeability.

[0004] However, these methods all have their own shortcomings when measuring porosity and permeability. Direct methods can quickly obtain porosity and permeability under different effective stresses, but they cannot analyze the evolution of pore size distribution. The disadvantages of conventional nuclear magnetic resonance (NMR) methods include: first, determining the parameters in the model requires repeated experiments with multiple cores, making parameter determination complex; second, when measuring rock samples from different reservoirs, parameters need to be redefined for better results, making it even more cumbersome; third, the results vary greatly for cores with poor heterogeneity; and fourth, this model is typically used to measure porosity and permeability under normal pressure, with limited application in overburden pressure porosity and permeability testing.

[0005] Patents CN113848158A (Two-dimensional large rock model porosity distribution testing method and device), CN116792091A (A method and application for evaluating the porosity of clastic rock reservoirs), CN116698890A (A variable porosity digital core modeling method based on conditional variational autoencoder), CN116413184A (A method for rapidly evaluating the total porosity, hydrocarbon-bearing porosity, and permeability of shale), CN110222368B (A method for calculating the three-dimensional porosity and permeability of cores using two-dimensional slices), CN114096828A (Laboratory measurement of dynamic fracture porosity and permeability changes in rock core samples), and CN105606513B (A method for determining the sensitivity of permeability and porosity of fractured rock mass to effective stress) all have the above-mentioned shortcomings. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a method for determining porosity and permeability of unconventional core samples under different net confining pressures.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0008] A method for determining porosity and permeability under different confining pressures includes the following steps:

[0009] Step (1): Use a conventional porosity and permeability meter to measure the porosity and permeability at atmospheric pressure or a certain pressure point as initial values;

[0010] Step (2): Take the pressure in step (1) as the initial pressure point for the nuclear magnetic resonance experiment, obtain the T2 spectrum data at this pressure point, and calculate the average T2 value;

[0011] Step (3): Obtain T2 spectrum data at different pressure points and calculate their average T2 values ​​respectively;

[0012] Step (4): Establish a stress-related mathematical model of porosity and permeability based on the initial values ​​obtained in steps (1) and (2);

[0013] Step (5): Combine the average T2 obtained in step (3) with the mathematical model to calculate the porosity and permeability under different confining pressures.

[0014] Furthermore, the permeability test data of the core analysis mentioned in step (1) is obtained in accordance with the procedure in the standard "Core Analysis Methods SY / T5336-2006".

[0015] Furthermore, the nuclear magnetic resonance T2 spectrum experimental data of the core analysis described in steps (2) and (3) were obtained in accordance with the procedures specified in the standard "Laboratory Measurement Specification for Nuclear Magnetic Resonance Parameters of Rock Samples SY / T6490-2007".

[0016] The formula for calculating the geometric mean of T2 in nuclear magnetic resonance imaging is as follows:

[0017]

[0018] In the formula, T 2gm The geometric mean of the T2 NMR spectrum is given in milliseconds (ms); φ i For the corresponding component T 2i Porosity component, in %; φ nmr NMR porosity, expressed as a percentage.

[0019] The formula for calculating NMR porosity is as follows:

[0020]

[0021] In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max This represents the termination value of the T2 spectrum relaxation time, in milliseconds (ms).

[0022] Furthermore, the mathematical model established in step (4) is a stress-related porosity and permeability original model:

[0023]

[0024]

[0025] In the formula, φ represents porosity, in %; k represents permeability, in mD; φ o Initial porosity, in %; k0, initial permeability, in mD; C p Δσ is the pore compressibility coefficient, in MPa⁻¹; Δσ is the effective stress change, in MPa.

[0026] Pore ​​compressibility coefficient C p Defined as:

[0027]

[0028] In the formula, φ is porosity, in %; σ is effective stress, in MPa.

[0029] The porosity compressibility can be written as:

[0030]

[0031] In the formula, r is the capillary radius, in μm; n is the number of capillaries per unit area, n = N / A; N is the number of capillaries in the hypothetical rock; A is the cross-sectional area of ​​the flow through the hypothetical rock, in cm²; C p σ is the pore compressibility coefficient, in MPa⁻¹; σ is the effective stress, in MPa.

[0032] Nuclear magnetic resonance T2 spectra can reflect the aperture distribution. Replacing the radius r in the formula with the average value of T2, we get:

[0033]

[0034] In the formula, T2 is the geometric mean value under the initial pressure, in milliseconds (ms). Δσ represents the geometric mean value under the current pressure, in milliseconds (ms); Δσ represents the effective stress change, in MPa.

[0035] Therefore, by combining the original stress-related porosity and permeability model, an innovative porosity and permeability model related to the geometric mean of nuclear magnetic resonance T2 can be obtained:

[0036]

[0037]

[0038] In the formula, T2 is the geometric mean value under the initial pressure, in milliseconds (ms). φ is the geometric mean at the current pressure, in ms; φ is the porosity, in %; k is the permeability, in mD; φ is the initial porosity, in %; k0 is the initial permeability, in mD.

[0039] If the porosity of the tested core sample is very small, the innovative model can be further simplified to:

[0040]

[0041]

[0042] In the formula, T2 is the geometric mean value under the initial pressure, in milliseconds (ms). The geometric mean value under the current pressure is expressed in milliseconds (ms); φ represents porosity in percent; k represents permeability in mD; φ o The initial porosity is expressed as a percentage (%); k0 is the initial permeability, expressed as mD. Very low porosity refers to 10% of the initial porosity.

[0043] Compared with the prior art, the beneficial effects of the technical solution of the present invention are as follows:

[0044] This invention obtains porosity and permeability under initial pressure through core analysis, then calculates the geometric mean of T2 using nuclear magnetic resonance (NMR) T2 spectral data under different net pressures, and finally combines this with the mathematical model proposed in this invention to calculate the porosity and permeability of the core under different net confining pressures. This method requires only an initial porosity and permeability value, as well as the geometric mean of T2 under different stress states, without the need for repeated parameter calibration. It overcomes the cumbersome parameter determination problem of traditional classical NMR porosity and permeability models and enables rapid measurement of porosity and permeability of cores under different stress states. It shows good results for both dense sandstone and shale samples. Attached Figure Description

[0045] Figure 1 The T2 nuclear magnetic resonance spectra of Shale No. 1 under different pressures as described in this embodiment of the invention;

[0046] Figure 2 The T2 nuclear magnetic resonance spectra of Shale No. 2 under different pressures as described in this embodiment of the invention;

[0047] Figure 3 This is a comparison diagram of the calculated porosity and core analysis porosity of two shale rocks described in an embodiment of the present invention.

[0048] Figure 4 This is a comparison chart of the calculated permeability and core analysis permeability of two shale rocks described in an embodiment of the present invention. Detailed Implementation

[0049] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments. The content mentioned in the embodiments is not intended to limit the present invention.

[0050] This invention provides a method for determining the porosity and permeability of shale cores under different net confining pressures, comprising the following steps:

[0051] Step (1): Perform routine physical property tests on shale cores. The core porosity and permeability analysis is conducted according to the procedures specified in the standard "Core Analysis Methods SY / T5336-2006" to obtain porosity and permeability under confining pressures of 0.5, 2, 5, 7, 10, and 15 MPa. The porosity and permeability at 0.5 MPa are used as initial values, and the values ​​at other pressures will be compared with the calculated porosity and permeability.

[0052] Step (2): Perform nuclear magnetic resonance (NMR) T2 spectral experiments on water-saturated shale cores to obtain NMR T2 spectral data. The NMR T2 experiments were conducted according to the procedures specified in the standard "Laboratory Measurement Specification for Nuclear Magnetic Resonance Parameters of Rock Samples SY / T6490-2007" to obtain T2 spectral data at 0.5 MPa. The average T2 value was calculated as the initial value for the NMR experiment.

[0053] The formula for calculating the geometric mean of T2 in nuclear magnetic resonance imaging is as follows:

[0054]

[0055] In the formula, T 2gm The geometric mean of the T2 NMR spectrum is given in milliseconds (ms); φ i For the corresponding component T 2i Porosity component, in %; φ nmr NMR porosity, expressed as a percentage.

[0056] The formula for calculating NMR porosity is as follows:

[0057]

[0058] In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max This represents the termination value of the T2 spectrum relaxation time, in milliseconds (ms).

[0059] Step (3): Using the same method as in step (2), obtain the T2 spectrum experimental data of tight sandstone cores and shale cores under confining pressures of 2, 5, 7, 10, and 15 MPa, and calculate their average T2 values ​​respectively. Figure 1-2 As shown.

[0060] Step (4): Combine the initial data obtained in Step (1) and Step (2) to establish mathematical models for tight sandstone cores and shale cores.

[0061] The stress-related porosity and permeability model for Shale No. 1 is as follows:

[0062]

[0063]

[0064] In the formula, φ is the geometric mean under the current pressure, in milliseconds (ms); φ is the porosity, in %; k is the permeability, in mD.

[0065] The stress-related porosity and permeability model for Shale No. 2 is as follows:

[0066]

[0067]

[0068] In the formula, φ is the geometric mean under the current pressure, in milliseconds (ms); φ is the porosity, in %; k is the permeability, in mD.

[0069] Step (5): Substitute the geometric mean T2 values ​​of the two shale cores under confining pressures of 2, 5, 7, 10, and 15 MPa into their respective mathematical models to calculate the porosity and permeability under the corresponding pressures. A comparison of the calculated porosity and permeability with the measured results can be found in [link to relevant documentation]. Figure 3-4 .

[0070] The results of conventional physical property experiments and nuclear magnetic resonance T2 spectroscopy experiments on the core are shown in Table 1.

[0071] Table 1

[0072]

[0073]

[0074] The results demonstrate that this invention provides a method for determining core porosity and permeability based on the geometric mean of T2 values ​​from nuclear magnetic resonance (NMR). This method requires only the core porosity and permeability at a specific pressure point as initial values. It utilizes NMR measurements of T2 spectra under different net confining pressures and calculates the geometric mean of T2 values ​​to quantitatively characterize changes in pore size distribution. Combined with the mathematical model established in this invention, it enables rapid and accurate quantitative calculation of core porosity and permeability under different net confining pressures. Furthermore, the parameters are simple to determine, and the method demonstrates good performance for both tight sandstone and shale cores.

[0075] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0076] It should be understood that the above detailed description of the technical solutions of the present invention with reference to preferred embodiments is illustrative and not restrictive. Those skilled in the art can modify the technical solutions described in the embodiments or make equivalent substitutions for some of the technical features based on reading this specification; however, these modifications or substitutions do not cause the essence of the corresponding technical solutions to depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining porosity and permeability of unconventional core samples under different net confining pressures, characterized in that, Includes the following steps: Step (1): Measure the porosity and permeability at a certain pressure point as initial values; Step (2): Take the pressure in step (1) as the initial pressure point for the nuclear magnetic resonance experiment, obtain the nuclear magnetic resonance T2 spectrum data at this pressure point, and calculate the average T2 value; Step (3): Obtain T2 spectrum data at different pressure points and calculate their average T2 values ​​respectively; Step (4): Establish a stress-related mathematical model of porosity and permeability based on the initial values ​​obtained in Step (1) and Step (2); Step (5): Combine the average T2 obtained in step (3) with the mathematical model to calculate the porosity and permeability under different confining pressures; The formula for calculating the average T2 value of nuclear magnetic resonance is as follows: In the formula, T 2gm The value is the geometric mean of the nuclear magnetic resonance T2 spectrum, expressed in milliseconds (ms). For the corresponding component T 2i The porosity component, in % %. NMR porosity, in % The formula for calculating NMR porosity is as follows: In the formula, S is the T2 spectral amplitude, in %; T2 is the transverse relaxation time measured by NMR, in ms; T 2min The initial value of the T2 spectrum relaxation time is given in milliseconds (ms). 2max The T2 spectrum relaxation time termination value, in ms; The mathematical model in step (4) is a stress-related porosity and permeability model. The original model is as follows: In the formula, Porosity, expressed as % Permeability, in mD; Initial porosity, in % % Initial permeability, in mD; The pore compressibility coefficient is expressed in MPa⁻¹. This represents the effective stress change, expressed in MPa. Pore ​​compressibility Defined as: In the formula Effective stress, in MPa; The porosity compressibility coefficient is written as: In the formula, r is the capillary radius in μm; n is the number of capillaries per unit area, n = N / A; N is the number of capillaries in the imaginary rock; and A is the cross-sectional area of ​​the flow through the imaginary rock in cm². 2 ; Nuclear magnetic resonance T2 spectra can reflect the aperture distribution. Using the average value of T2 instead of the radius r, we get: In the formula, T2 is the geometric mean value under the initial pressure, in milliseconds (ms). This is the geometric mean value under the current pressure, expressed in milliseconds. Combining the original stress-related porosity and permeability model, the porosity and permeability with the geometric mean of nuclear magnetic resonance T2 can be obtained: 。 2. The method according to claim 1, characterized in that, The tested core samples had very low porosity. The porosity and permeability were determined by the geometric mean of nuclear magnetic resonance T2: 。 3. The method for determining porosity and permeability of unconventional cores under different net confining pressures as described in any one of claims 1-2, applied to core measurement.

4. The application according to claim 3, characterized in that, The core is a core of dense sandstone and / or shale.

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