CN105241913A

CN105241913A - Nuclear magnetic resonance quantitative analysis method for rock micro-crack damage variable

Info

Publication number: CN105241913A
Application number: CN201510655268.3A
Authority: CN
Inventors: 王萍; 屈展; 王亮; 黄海; 高辉
Original assignee: Xian Shiyou University
Current assignee: Xian Shiyou University
Priority date: 2015-10-10
Filing date: 2015-10-10
Publication date: 2016-01-13
Anticipated expiration: 2035-10-10
Also published as: CN105241913B

Abstract

The NMR quantitative analysis method of rock micro-crack damage variables first processes the sample, soaks the sample in distilled water, and then performs NMR detection. The spin echo train attenuation signal is obtained by performing CPMG pulse sequence test on the sample. The attenuation signal of the spin echo series is inverted to obtain the distribution diagram and spectral area value of the T2 spectrum _; the corresponding relationship between the relaxation time T2 and the pore size r is analyzed, and according to the fact that the spectral peak area is proportional to the number of micro _- crack pores, the present invention The rock damage variable formula characterized by the NMR transverse relaxation time T ₂ spectrum is established, which provides a quantitative analysis method for identifying the damage of rock materials.

Description

NMR Quantitative Analysis Method of Rock Micro-fracture Damage Variables

技术领域technical field

本发明涉及岩石细观损伤力学领域，尤其涉及岩石微裂缝损伤变量的核磁共振定量分析方法。The invention relates to the field of rock mesoscopic damage mechanics, in particular to a nuclear magnetic resonance quantitative analysis method for rock micro-crack damage variables.

背景技术Background technique

工程实践和研究表明，由于岩石类材料存在有初始微缺陷，从开始变形直至屈服破坏是一个损伤累积和逐渐劣化的过程，是一个损伤随时间由小到大直至破坏的量变到质变过程。Engineering practice and research have shown that due to the initial micro-defects in rock materials, the process from initial deformation to yield failure is a process of damage accumulation and gradual deterioration, and it is a process of quantitative change to qualitative change from small to large to failure over time.

为了观察和研究岩石内部结构的损伤演化直至完全破裂的过程，国内外学者通过各种岩石细观力学试验进行了研究。茅献彪采用细观力学试验方法，利用光学显微镜和SEM扫描电镜对膨胀岩进行了分析，研究了膨胀岩在间接拉伸、单轴压缩、三轴压缩和长期流变试验过程中的损伤破坏规律。冯夏庭、陈四利等观测了岩石在受压状态及水、化学溶液作用下，表面细观破裂破坏过程，详细探讨了其动态损伤和破裂的机理。赵永红进行了灰岩裂纹扩展和破裂机理细观试验的研究。葛修润、任建喜等在国内首次利用CT实时观测了岩石三轴压缩破坏全过程，分析得到了岩石损伤演化的初步规律。石秉忠采用CT成像技术，微观揭示硬脆性泥页岩水化过程中裂缝的发展规律。这些研究多对损伤进行了定性的分析，没有进行定量的研究。杨更社以细观损伤力学为基础，建立以CT数为函数的损伤变量，为识别岩石损伤提供了新的定量分析方法。In order to observe and study the process of the damage evolution of the internal structure of the rock until it is completely broken, scholars at home and abroad have conducted research through various rock mesomechanics tests. Mao Xianbiao used the mesomechanics test method to analyze the expansive rock by optical microscope and SEM scanning electron microscope, and studied the damage and failure law of the expansive rock in the process of indirect tension, uniaxial compression, triaxial compression and long-term rheological test. Feng Xiating, Chen Sili, etc. observed the microscopic fracture process of rocks under pressure and the action of water and chemical solutions, and discussed in detail the mechanism of dynamic damage and fracture. Zhao Yonghong carried out the mesoscopic test of limestone crack propagation and fracture mechanism. For the first time in China, Ge Xiurun and Ren Jianxi used CT to observe the whole process of rock triaxial compression failure in real time, and analyzed the preliminary law of rock damage evolution. Shi Bingzhong used CT imaging technology to microscopically reveal the development law of fractures in the hydration process of hard and brittle shale. Most of these studies have carried out qualitative analysis on damage, but no quantitative research has been carried out. Based on mesoscopic damage mechanics, Yang Gengshe established a damage variable with CT number as a function, which provided a new quantitative analysis method for identifying rock damage.

核磁共振技术(NMR)作为研究岩石细观结构的新型检测方式，具有无损、反复和快速等优点。目前核磁共振技术在石油工程领域，主要通过对岩石孔隙结构、储层岩石孔隙流体特性等方面的研究，来进行储层评价及录井测井方面的应用。目前还未见将其应用于定量的分析岩石微裂缝损伤机制的研究。在损伤力学中，损伤变量是非常重要的变量，对于损伤演变的过程可以进行合理的描述，也是损伤理论建立的基础，所以对它进行合理的定义是非常有必要的。Nuclear Magnetic Resonance (NMR), as a new detection method for studying rock mesostructure, has the advantages of non-destructive, repetitive and fast. At present, in the field of petroleum engineering, nuclear magnetic resonance technology is mainly used for reservoir evaluation and mud logging through the research of rock pore structure and reservoir rock pore fluid characteristics. At present, there is no research on applying it to quantitatively analyze the damage mechanism of rock micro-cracks. In damage mechanics, the damage variable is a very important variable, which can reasonably describe the damage evolution process and is also the basis for the establishment of damage theory, so it is very necessary to define it reasonably.

发明内容Contents of the invention

为了克服上述现有技术的难点，本发明的目的在于提供岩石微裂缝损伤变量的核磁共振定量分析方法，建立由核磁共振横向弛豫时间T₂谱表征的岩石损伤变量公式，为识别岩石材料的损伤提供了新的定量分析方法。In order to overcome the difficulties of the above-mentioned prior art, the object of the present invention is to provide the nuclear magnetic resonance quantitative analysis method of the rock micro-crack damage variable, set up by the nuclear magnetic resonance transverse relaxation time T The rock damage variable _formula characterized by the spectrum is used to identify the rock material Damage provides new quantitative analysis methods.

为了达到上述目的，本发明采取的技术方案为：In order to achieve the above object, the technical scheme that the present invention takes is:

岩石微裂缝损伤变量的核磁共振定量分析方法，包括以下步骤：A nuclear magnetic resonance quantitative analysis method for damage variables of rock micro-cracks, comprising the following steps:

第一步，按行业标准将试样加工成直径为25毫米、长为50毫米的圆柱体；将试样浸泡在蒸馏水中，分别在浸泡10min、30min、1h、2h、4h、6h、8h、1d、3d、5d不同时间后取出试样；对经过浸泡的试样进行核磁共振检测，通过对试样进行CPMG脉冲序列测试，得到自旋回波串衰减信号；利用核磁共振弛豫时间反演拟合软件对自旋回波串衰减信号进行反演，得到T₂谱的分布图、谱面积值和各峰所占比例值；利用MiniMR核磁共振成像软件得到同一试样不同浸泡时间的核磁共振成像；The first step is to process the sample into a cylinder with a diameter of 25 mm and a length of 50 mm according to industry standards; soak the sample in distilled water for 10 min, 30 min, 1 h, 2 h, 4 h, 6 h, 8 h, After 1d, 3d, and 5d, the samples were taken out at different times; NMR detection was performed on the soaked samples, and the spin echo train attenuation signal was obtained by performing CPMG pulse sequence tests on the samples; the NMR relaxation time inversion was used to simulate Combine software to invert the spin echo train attenuation signal to obtain the T2 spectrum distribution map, spectral area value and the proportion value of each peak; use _MiniMR nuclear magnetic resonance imaging software to obtain the nuclear magnetic resonance imaging of the same sample with different soaking times;

第二步，根据核磁共振原理,T₂弛豫由表面弛豫决定，表面驰豫与介质表面积有关，多孔介质孔隙表面积S与孔隙体积V之比为介质比表面，介质比表面越大，则驰豫越强，反之亦然，T₂表面表示为：In the _second step, according to the principle of nuclear magnetic resonance, the T2 relaxation is determined by the surface relaxation, and the surface relaxation is related to the surface area of the medium. The ratio of the pore surface area S of the porous medium to the pore volume V is the medium specific surface, and the larger the medium specific surface, then _The stronger the relaxation, and vice versa, the T2 surface is expressed as:

式中ρ₂为T₂表面驰豫强度；(S/V)_孔隙为孔隙表面积S与孔隙体积V之比，where _ρ2 is the surface relaxation intensity of T2 _; (S/V) _pore is the ratio of pore surface area S to pore volume V,

继而得到T₂与孔径r的关系为：Then the relationship between T2 and aperture r is obtained as _:

Fs称为几何形状因子，由上式可见孔隙内流体的弛豫时间和孔隙空间大小有关,孔隙越小,比面积越大,表面相互作用的影响越强烈,T₂时间也越短，弛豫时间T₂和孔径r是一一对应的，利用T₂分布来评价孔隙裂纹大小、分布；Fs is called the geometry factor. From the above formula, it can be seen that the relaxation time of the fluid in the pores is related to the size of the pore space. _The smaller the pores, the larger the specific area, the stronger the influence of surface interaction, and the shorter the T2 time. The time T ₂ and the pore diameter r are in one-to-one correspondence, and the T ₂ distribution is used to evaluate the size and distribution of pore cracks;

第三步，建立微裂纹密度分布函数n(r，t)，对理想微裂纹系统进行统计描述，n表示在t时刻时，单位体积内尺度在r～r+dr范围内的裂纹数n(r，t)dr，在损伤初期，略去裂纹间相关效应，成核过程和扩展过程决定了n的演化规律，The third step is to establish the microcrack density distribution function n(r, t) to statistically describe the ideal microcrack system, n represents the number of cracks per unit volume within the range of r~r+dr at time t ( r, t)dr, in the early stage of damage, the correlation effect between cracks is omitted, the nucleation process and the expansion process determine the evolution law of n,

考察孔径r所张成的一维相空间中相体元(r，r+Δr)内微裂纹数密度变化，Investigate the variation of the number density of microcracks in the phase volume element (r, r+Δr) in the one-dimensional phase space spanned by the aperture r,

${&Integral; &Integral;}_{r r}^{r r + + Δ Δ r r} n no (({r r}^{' '},, t t)) {dr dr}^{' '} - - - - - - ((33))$

第四步，设连续损伤D用微损伤数密度来表示：In the fourth step, the continuous damage D is expressed by the number density of micro-damages:

$D D. = = {&Integral; &Integral;}_{00}^{∞ ∞} r r n no ((t t,, r r)) d d r r - - - - - - ((44))$

将第二步中的式(2)中的r代入上式(4)则得Substituting r in the formula (2) in the second step into the above formula (4), we get

$D D. = = {&Integral; &Integral;}_{{T T}_{00}}^{{T T}_{22}} {F f}_{S S} {T T}_{22} n no ((t t,, {T T}_{22})) {dT dT}_{22} - - - - - - ((55))$

第五步，对第一步反演得到的T₂谱面积进行分析，核磁共振横向弛豫时间T₂谱的积分面积正比于试样中所含流体的多少,T₂谱中X坐标表示弛豫时间T₂值大小，谱峰的位置与孔径大小有关，由此得到微损伤扩展前沿在Δt内新扩展的面积The fifth step is to analyze the area of the T ₂ spectrum obtained from the inversion of the first step. The integral area of the NMR transverse relaxation time T ₂ spectrum is proportional to the amount of fluid contained in the sample, and the X coordinate in the T ₂ spectrum represents the relaxation time. _The value of time T2, the position of the spectral peak is related to the pore size, and thus the newly expanded area of the micro-damage expansion front within Δt

S≈∫F_Sn(t,T₂)dT₂(6)S≈∫F _S n(t,T ₂ )dT ₂ (6)

第六步，根据(5)和(6)两式，建立以T₂谱表征的损伤变量为In the sixth step, according to the _two formulas (5) and (6), the damage variable represented by the T2 spectrum is established as

${D D.}_{T T} = = \frac{{S S}_{{T T}_{22}} - - {S S}_{{T T}_{00}}}{{S S}_{{T T}_{22}}} = = 11 - - \frac{{S S}_{{T T}_{00}}}{{S S}_{{T T}_{22}}} - - - - - - ((77))$

S_T0由核磁共振测量初始损伤时的T₂谱积分面积，S_T2为经过水化浸泡后由核磁共振测量水化损伤的T₂谱积分面积。S _T0 is the integrated area of T ₂ spectrum measured by NMR at the initial damage, and S _T2 is the integrated area of T ₂ spectrum measured by NMR for hydration damage after hydration soaking.

本发明的有益效果：建立由核磁共振横向弛豫时间T₂谱表征的岩石损伤变量公式，为识别岩石材料的损伤提供了新的定量分析方法。Beneficial effects of the present invention: the rock damage variable formula characterized by the nuclear magnetic resonance transverse relaxation time T ₂ spectrum is established, and a new quantitative analysis method is provided for identifying the damage of rock materials.

附图说明Description of drawings

图1为实施例的岩样浸泡后的T₂谱。Fig. ₁ is the T2 spectrum of the rock sample soaked in the embodiment.

图2为实施例的试样浸泡1h的核磁成像图。Fig. 2 is the nuclear magnetic imaging figure of the sample soaked for 1 hour in the embodiment.

图3为实施例的试样浸泡8h的核磁成像图。Fig. 3 is the NMR image of the sample soaked for 8 hours in the embodiment.

图4为实施例的试样浸泡1d的核磁成像图。Fig. 4 is a nuclear magnetic imaging image of the sample soaked 1d in the embodiment.

图5为实施例的试样浸泡3d的核磁成像图。Fig. 5 is a nuclear magnetic imaging image of the sample soaked 3d in the embodiment.

图6为实施例的试样浸泡5d的核磁成像图。Fig. 6 is a nuclear magnetic imaging image of the sample soaked 5d in the embodiment.

具体实施方式detailed description

下面结合实施例及附图对本发明做详细描述。The present invention will be described in detail below in conjunction with the embodiments and accompanying drawings.

第一步，按行业标准将试样加工成直径为25毫米、长为50毫米的圆柱体；将试样浸泡在蒸馏水中，分别在浸泡10min、30min、1h、2h、4h、6h、8h、1d、3d、5d不同时间后取出试样；对经过浸泡的试样进行核磁共振检测，通过对试样进行CPMG脉冲序列测试，得到自旋回波串衰减信号，自旋回波串衰减信号是不同大小孔隙内水信号的叠加；利用核磁共振弛豫时间反演拟合软件对自旋回波串衰减信号进行反演，得到T₂谱的分布图、谱面积值和各峰所占比例值；利用MiniMR核磁共振成像软件得到同一试样不同浸泡时间的核磁共振成像；The first step is to process the sample into a cylinder with a diameter of 25 mm and a length of 50 mm according to industry standards; soak the sample in distilled water for 10 min, 30 min, 1 h, 2 h, 4 h, 6 h, 8 h, Take out the samples after 1d, 3d, and 5d at different times; conduct nuclear magnetic resonance detection on the soaked samples, and obtain spin echo train attenuation signals by performing CPMG pulse sequence tests on the samples, and the spin echo train attenuation signals are of different sizes The superposition of water signals in the pores; use the NMR relaxation time inversion fitting software to invert the attenuation signal of the spin echo series, and obtain the distribution map of the T2 spectrum, the spectral area value and the proportion of each peak; use the _MiniMR Nuclear magnetic resonance imaging software obtains nuclear magnetic resonance imaging of the same sample at different immersion times;

第二步，根据核磁共振原理,T₂弛豫由表面弛豫决定，表面驰豫与介质表面面积有关，介质比表面(多孔介质孔隙表面积S与孔隙体积V之比)越大，则驰豫越强，反之亦然，T₂表面表示为：In the second step, according to the principle of nuclear magnetic resonance, T ₂ relaxation is determined by surface relaxation, which is related to the surface area of the medium. _The stronger and vice versa, the T2 surface is expressed as:

继而得到T₂与孔径r的关系为：Then the relationship between T ₂ and aperture r is obtained as:

第五步，参照图1，T₂谱中X坐标表示弛豫时间T₂值大小，谱峰的位置与孔径大小有关，小孔隙组分别对应较小的T₂值，大孔隙组分别对应较大的T₂值，能反映岩石的孔隙结构，Y坐标表示信号幅度，谱峰幅度高，对应峰面积大，则对应孔径的孔隙数量就多，反之则少。谱峰面积的大小与对应孔径的孔隙数量有关，由此得到微损伤扩展前沿在Δt内新扩展的面积 _The fifth step, referring to Figure ₁ , the X coordinate in the T2 spectrum represents the relaxation time T2 value, the position of the spectrum peak is related to the pore size, the small pore group corresponds to the smaller _T2 value, and the large pore group corresponds to the larger T2 value. _A large T2 value can reflect the pore structure of the rock, and the Y coordinate indicates the signal amplitude. If the spectral peak amplitude is high and the corresponding peak area is large, the number of pores corresponding to the pore diameter will be large, and vice versa. The size of the spectral peak area is related to the number of pores corresponding to the pore size, and thus the newly expanded area of the micro-damage expansion front within Δt

S≈∫F_Sn(t,T₂)dT₂(6)S≈∫F _S n(t,T ₂ )dT ₂ (6)

对第一步反演得到的T₂谱面积进行分析，核磁共振横向弛豫时间T₂谱的积分面积正比于试样中所含流体的多少,它等于或略小于试样的有效孔隙度，对应孔径的孔隙数量与峰面积的大小有关，Analyze the T2 spectrum area obtained by the inversion in the first step. _The integral area of the NMR transverse relaxation time T2 spectrum is proportional to the amount of fluid contained in the sample, which is equal to or slightly smaller _than the effective porosity of the sample. The number of pores corresponding to the pore diameter is related to the size of the peak area,

附表1为不同浸泡时间下岩石核磁共振谱面积Attached Table 1 shows the areas of NMR spectra of rocks under different immersion times

从附表1可以看出T₂谱面积是逐渐增大的，表明随着浸泡时间的延长,试样孔隙体积增大，对应小尺寸微孔隙的第一个峰占总面积的90％左右，表明小尺寸的微孔隙占绝大多数，1h浸泡后，第一峰所占比例变化不大，而第二峰相对变化较大，表明岩样内部大尺寸孔隙增长较快，即岩样内部出现明显的微裂纹损伤扩展，浸泡时间超过8h以后，T₂谱面积又发生明显的变化，并且出现了第三个峰，说明同时并伴随微裂纹的扩展，又诱发和产生了一些新的分叉性微裂纹，此时试样中的裂纹数量较多且长，致使试样内部损伤加大，1d之后T₂谱面积的继续变大，对应小尺寸微孔隙的第一个峰占比例也明显增加，但对应大尺寸孔隙第二峰占比例变小，第三峰甚至消失，说明微孔隙还在不断的产生和扩展，大尺寸孔隙裂纹已经归并贯通到宏观破坏，说明试样的水化损伤前期变化较大，后期变化缓慢；It can be seen from the attached table ₁ that the area of the T2 spectrum increases gradually, indicating that with the prolongation of the soaking time, the pore volume of the sample increases, and the first peak corresponding to the small-sized micropores accounts for about 90% of the total area. It shows that small-sized micropores account for the vast majority. After soaking for 1 hour, the proportion of the first peak does not change much, while the relative change of the second peak shows that the large-sized pores inside the rock sample grow faster, that is, the inside of the rock sample appears Obvious microcrack damage expansion, after soaking for more than ₈ hours, the T2 spectrum area changed significantly, and a third peak appeared, indicating that at the same time and accompanied by the expansion of microcracks, some new bifurcations were induced and produced At this time, the number of cracks in the sample is large and long, which increases the internal damage of the sample. After 1d, the T2 spectrum area continues to increase, and the proportion of the first peak corresponding to small _- sized micropores is also obvious. increase, but the proportion of the second peak corresponding to the large-sized pores becomes smaller, and the third peak even disappears, indicating that the micro-pores are still continuously generated and expanding. Larger changes in the early stage and slow changes in the later stage;

S_T0由核磁共振测量初始损伤时的T₂谱积分面积，S_T2为经过水化浸泡后由核磁共振测量水化损伤的T₂谱积分面积，初始状态下D_T＝0：而当试件内部损伤发展到极限状态时(损伤破坏)，则认为有则D_T＝1,但实际上在有效面积消失以前，试件已不能继续维持结构的平衡，所以破坏时DT<1。S _T0 is the T ₂ spectrum integral area measured by nuclear magnetic resonance at the time of initial damage, and S _T2 is the T ₂ spectrum integral area of hydration damage measured by NMR after hydration soaking. In the initial state D _T ＝0: When the internal damage of the specimen develops to the limit state (damage failure), it is considered that there is but _DT = 1, but in fact, before the effective area disappears, the specimen cannot continue to maintain the balance of the structure, so DT<1 when it is destroyed.

将第五步得到的核磁T₂谱面积值代入式(7)得到岩石微裂缝损伤变量，如附表2所示。Substitute the NMR T2 spectrum area value obtained in the fifth step into _formula (7) to obtain the damage variable of rock micro-cracks, as shown in Table 2.

附表2为岩石微裂缝损伤变量Attached Table 2 shows the rock micro-fracture damage variables

公式(7)实质上是将密度的变化用核磁共振T₂波谱面积的变化来反映，从而解决了材料损伤变化难以测量问题,从附表2中可以看出随着浸泡时间的延长，相应损伤变量值也越大。Formula ( ₇ ) essentially reflects the change of density with the change of NMR T2 spectral area, thus solving the problem that the change of material damage is difficult to measure. The variable value is also larger.

与第一步得到核磁共振成像结果进行对比分析，参照图2、图3图4、图5、图6，分别为浸泡1h、8h、1d、3d、5d的岩样核磁共振成像图，图像中黑色为底色，发白的区域为水分子所在区域，代表的是孔隙范围，图像的亮度反映了试样中含水量的多少,白色亮斑越多，意味着岩石孔隙越大，反之，则孔隙越小，这样能直观看出试样内部的孔隙大小分布情况，展示出了试样在水化作用下，内部结构的动态损伤演化过程。随着浸泡时间的延长，岩石损伤在逐步扩大。这与本文根据(7)计算出的T₂谱表征的损伤变量D_T附表2所示结果一致。Compare and analyze with the MRI results obtained in the first step. Refer to Figure 2, Figure 3, Figure 4, Figure 5, and Figure 6, which are the MRI images of rock samples soaked for 1h, 8h, 1d, 3d, and 5d respectively. Black is the background color, and the whitish area is the area where the water molecules are located, representing the pore range. The brightness of the image reflects the water content in the sample. The more white bright spots, the larger the rock pores, and vice versa. The smaller the pores, the smaller the pore size distribution inside the sample can be seen intuitively, which shows the dynamic damage evolution process of the internal structure of the sample under hydration. With the prolongation of immersion time, rock damage is gradually expanding. This is consistent with the results shown in Table 2 of the damage variable D _T represented by the T ₂ spectrum calculated according to (7).

本发明定量的给出了不同浸泡时间下的损伤变量值，为识别岩石材料的损伤和定量描述提供了新的方法。建立损伤变量与应力、应变之间的关系将为岩石损伤扩展规律及损伤本构关系的建立提供坚实的基础。The invention quantitatively gives the damage variable values under different immersion times, and provides a new method for identifying the damage of rock materials and quantitatively describing them. Establishing the relationship between damage variables and stress and strain will provide a solid foundation for the establishment of rock damage propagation law and damage constitutive relationship.

Claims

1. the nmr quantitative analysis method of rock microfracture damage variable, is characterized in that, comprise the following steps:

The first step, is processed into sample the right cylinder that diameter is 25 millimeters, length is 50 millimeters by industry standard; Sample is immersed in distilled water, after immersion 10min, 30min, 1h, 2h, 4h, 6h, 8h, 1d, 3d, 5d different time, takes out sample respectively; Magnetic resonance detection being carried out to the sample through soaking, by carrying out the test of CPMG pulse train to sample, obtaining spin echo string deamplification; Utilize NMR (Nuclear Magnetic Resonance) relaxation time reversal fitting software to carry out inverting to spin echo string deamplification, obtain T ₂the distribution plan composed, area under spectrum value and each peak proportion value, utilize MiniMR MRI software to obtain the Magnetic resonance imaging of the different soak time of same sample;

Second step, according to nuclear magnetic resonance principle, T ₂relaxation is determined by surface relaxation, and Surface Relaxation is relevant with media table area, and porous medium pore surface area S and the ratio of volume of voids V are Media Ratio surface, and Media Ratio surface is larger, then relaxation is stronger, and vice versa, T ₂surface is expressed as:

ρ in formula ₂for T ₂surface Relaxation intensity; (S/V) _holefor pore surface area S and the ratio of volume of voids V,

Then T is obtained ₂with the pass of aperture r be:

Fs is called geometrical form factors, and relevant with pore space size by the relaxation time of above formula visible hole inner fluid, hole is less, and specific area is larger, and the impact of surface interaction is stronger, T ₂time is also shorter, relaxation time T ₂be one to one with aperture r, utilize T ₂hole crackle size, distribution are evaluated in distribution;

3rd step, set up microcrack density distribution function n (r, t), carry out statistics to desirable micro-crack system and describe, n represents when t, the crackle number n (r of yardstick within the scope of r ~ r+dr in unit volume, t) dr, at early injury, omits correlation effect between crackle, nucleation process and expansion process determine the Evolution of n

Investigate the interior micro-crack number density of phase volume elements (r, r+ Δ r) in the aperture r institute one dimension phase space of opening to change,

{&Integral;}_{r}^{r + Δ r} n (r^{'}, t) {dr}^{'} - - - (3)

4th step, if continuous damage D micro-damage number density represents:

D = {&Integral;}_{h}^{\infty} r n (t, r) d r - - - (4)

R in formula (2) in second step is substituted into above formula (4) then obtain

D = {&Integral;}_{T_{0}}^{T_{2}} F_{S} T_{2} n (t, T) {dT}_{2} - - - (5)

5th step, to the T that first step inverting obtains ₂area under spectrum is analyzed, nuclear magnetic resonance T2 T ₂the integral area of spectrum to be proportional in sample contained fluid number, T ₂in spectrum, X-coordinate represents relaxation time T ₂value size, the position at spectrum peak is relevant with pore size, obtains the area of micro-damage expansion forward position new expansion in Δ t thus

S≈∫F _Sn(t,T ₂)dT ₂(6)

6th step, according to (5) and (6) two formulas, sets up with T ₂the damage variable that stave is levied is

D_{T} = \frac{S_{T_{2}} - S_{T_{0}}}{S_{T_{2}}} = 1 - \frac{S_{T_{0}}}{S_{T_{2}}} - - - (7)

S _t0by T during Nuclear Magnetic Resonance Measurement initial damage ₂spectral integral area, S _t2for the T damaged by Nuclear Magnetic Resonance Measurement aquation after aquation is soaked ₂spectral integral area.