A method, system, device, and storage medium for predicting the permeability of tight sandstone.

Abstract

This invention provides a method, system, device, and storage medium for predicting sandstone permeability. The method includes: acquiring a first or second permeability prediction model; acquiring the geometric mean of the pore radius or the NMR T2 distribution within the range of transverse relaxation time >40ms corresponding to a cumulative mercury saturation of 20% for the target sample, as well as the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size or the cumulative percentage distribution of the NMR pore size; acquiring the lower limit of the pore size of the movable fluid storage space of the target sample and using it as the boundary point for fractal analysis; combining the aforementioned cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size or the cumulative percentage distribution of the NMR pore size to determine the first or second fractal dimension of the target sample; determining the permeability of the target sample using the first permeability prediction model based on the aforementioned pore radius and first fractal dimension, or determining the permeability of the target sample using the second permeability prediction model based on the aforementioned geometric mean and second fractal dimension.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas field exploration and development technology, and specifically relates to a sandstone permeability prediction method, system, device and storage medium applicable to tight sandstone. Background Technology

[0002] For tight sandstone reservoirs, permeability is a crucial parameter for evaluating reservoir properties and seepage characteristics, and it is also key to tapping reservoir productivity and improving recovery rates. Tight sandstone reservoirs exhibit diverse pore types, complex pore structures, and strong heterogeneity, resulting in a complex and non-linear porosity-permeability relationship. Predictive methods using porosity-permeability statistical regression and well logging interpretation methods have relatively low accuracy, making permeability prediction for tight sandstone reservoirs an important and challenging task. Due to the complex pore structure and strong heterogeneity of tight sandstone reservoirs, their permeability varies widely, making prediction difficult. Therefore, there is an urgent need to develop permeability prediction models suitable for tight sandstone.

[0003] Existing permeability prediction models can be broadly categorized into three types: permeability prediction models based on high-pressure mercury intrusion porosimetry (HPMI), permeability prediction models based on nuclear magnetic resonance (NMR), and permeability prediction models based on fractal geometry. HPMI-based permeability prediction models use gas-measured porosity and optimal pore radius to predict permeability; their prediction accuracy depends solely on the choice of pore radius, thus having certain limitations. Existing HPMI-based permeability prediction models generally suffer from unsatisfactory prediction accuracy. NMR-based permeability prediction models use gas-measured porosity and pore structure parameters obtained from NMR experiments (geometric mean of T2 / volume ratio of mobile fluid to bound fluid / spectral relaxation time) to predict permeability. They are mostly used to evaluate well-sorted, porous sandstones, often requiring a close correlation between permeability and porosity, and are not suitable for dense sandstones. NMR-based permeability prediction models show unsatisfactory prediction results when used for dense sandstone permeability. Fractal dimension-based permeability prediction models use gas-measured porosity, the fractal dimension of macropores, and pore structure parameters obtained from nuclear magnetic resonance (NMR) (geometric mean of T2 / volume ratio of mobile fluid to bound fluid) to predict permeability. These models are often used to evaluate well-sorted, porous sandstones and typically require a close correlation between permeability and porosity. They are not suitable for dense sandstones. When performing piecewise fractal analysis of NMR data, a specific NMR T2 value is usually selected. 2cutoff Using the logarithm as the boundary point between different fractal segments neglects the contribution of some small pores to seepage, which has a certain impact on the accuracy of the permeability model; existing permeability prediction models based on fractal dimension do not perform well when used to predict the permeability of tight sandstone.

[0004] Therefore, it is still necessary to develop a permeability prediction model applicable to tight sandstone. Summary of the Invention

[0005] The purpose of this invention is to provide a method, system, device, and storage medium for predicting the permeability of dense sandstone.

[0006] To achieve the above objectives, the present invention provides the following four technical solutions.

[0007] In a first aspect, the present invention provides a method for predicting the permeability of sandstone, wherein the method includes:

[0008] Step S1: Obtain either a first permeability prediction model or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution within the range of >40ms.

[0009] Step S2: Obtain the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample or the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40ms;

[0010] Step S3: Obtain the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size or the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample;

[0011] Step S4: Obtain the lower limit of the pore size of the movable fluid storage space of the target sample;

[0012] Step S5: Based on the cumulative mercury saturation distribution of the high-pressure mercury injection pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, determine the fractal dimension of the movable fluid storage space of the target sample, which is the first fractal dimension of the target sample; or; based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, determine the fractal dimension of the movable fluid storage space of the target sample, which is the second fractal dimension of the target sample;

[0013] Step S6: Based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, determine the permeability of the target sample using a first permeability prediction model based on fractal theory; or: Based on the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40ms and the second fractal dimension of the target sample, determine the permeability of the target sample using a second permeability prediction model based on fractal theory.

[0014] Secondly, the present invention provides a sandstone permeability prediction system, the system comprising:

[0015] Model acquisition module: used to acquire either a first permeability prediction model or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution range >40ms.

[0016] First data acquisition module: used to acquire the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample or the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution of the target sample within the range of >40ms;

[0017] The second data acquisition module is used to acquire the cumulative mercury saturation distribution of the high-pressure mercury injection pore size or the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample.

[0018] Pore ​​diameter lower limit determination module: used to obtain the lower limit of the pore diameter of the movable fluid storage space of the target sample;

[0019] The fractal dimension determination module is used to determine the first fractal dimension of the target sample's movable fluid storage space based on the cumulative mercury saturation distribution of the high-pressure mercury injection pore size, using the lower limit of the movable fluid storage space's pore size as the boundary point for fractal analysis; or, based on the cumulative percentage distribution of the target sample's nuclear magnetic resonance pore size, using the lower limit of the movable fluid storage space's pore size as the boundary point for fractal analysis, the second fractal dimension of the target sample's movable fluid storage space is determined.

[0020] The permeability determination module is used to determine the permeability of a target sample based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, using a first permeability prediction model based on fractal theory; or, based on the geometric mean of the transverse relaxation time in the T2 distribution of the target sample's nuclear magnetic resonance within the range of >40ms and the second fractal dimension of the target sample, using a second permeability prediction model based on fractal theory.

[0021] Thirdly, the present invention provides a storage medium storing one or more programs that can be executed by one or more processors to implement the above-described sandstone permeability prediction method.

[0022] Fourthly, the present invention provides an apparatus suitable for performing the above-described sandstone permeability prediction method, the apparatus comprising:

[0023] The invention comprises a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The memory stores computer programs. When the processor executes the programs stored in the memory, it implements the sandstone permeability prediction method provided by this invention.

[0024] The technical solution provided by this invention uses fractal analysis based on high-pressure mercury intrusion pore size distribution and nuclear magnetic resonance pore size distribution to determine the fractal dimension within a specific pore range. Based on the fractal dimension, permeability is predicted by combining the pore radius corresponding to a cumulative mercury saturation of 20% and the geometric mean of the transverse relaxation time >40ms in the nuclear magnetic resonance T2 distribution. In a preferred embodiment, the pore radius corresponding to the optimal centrifugal force is defined as the lower limit of mobile fluid porosity, and its logarithm is used as the boundary point for fractal analysis, which better reflects the heterogeneity of the mobile fluid reservoir space. Compared with existing technologies, the technical solution provided by this invention is better applicable to the permeability determination of tight sandstone and has higher permeability determination accuracy. Attached Figure Description

[0025] Figure 1 A flowchart of a sandstone permeability prediction method provided in one embodiment of the present invention.

[0026] Figure 2 The graph shows the high-pressure mercury intrusion pore size distribution curve and the high-pressure mercury intrusion pore size cumulative mercury saturation distribution curve of the target sample in Example 1.

[0027] Figure 3 This is a schematic diagram showing the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample determined in Example 1.

[0028] Figure 4 The image shows the nuclear magnetic resonance T2 spectrum and the cumulative percentage distribution curve of T2 for the target sample in Example 1.

[0029] Figure 5 This is a distribution curve in Example 1 with cumulative normalized percentage as the abscissa and T2 and pore radius r as the ordinate.

[0030] Figure 6 The image shows the nuclear magnetic resonance pore size distribution curve and cumulative pore size percentage distribution of the target sample in Example 1.

[0031] Figure 7 The T2 spectra are obtained after centrifugation at different speeds in Example 1.

[0032] Figure 8 This is a diagram showing the fitting and determination of the first fractal dimension in Example 1.

[0033] Figure 9 This is a diagram showing the fitting and determination of the second fractal dimension in Example 1.

[0034] Figure 10 This is a graph showing the accuracy analysis of the permeability prediction results based on the first permeability prediction model in Experiment Example 1.

[0035] Figure 11 This is a graph showing the accuracy analysis of the permeability prediction results based on the second permeability prediction model in Experiment Example 1.

[0036] Figure 12 For example 1, based on r 10 Accuracy analysis chart of the model's penetration rate prediction results.

[0037] Figure 13 For example 1, based on r 25 Accuracy analysis chart of the model's penetration rate prediction results.

[0038] Figure 14 For example 1, based on r 35 Accuracy analysis chart of the model's penetration rate prediction results.

[0039] Figure 15 This is a graph showing the accuracy analysis of the permeability prediction results based on the Swanson model in Experiment Example 1.

[0040] Figure 16 For example 1, based on r apex Accuracy analysis chart of the model's penetration rate prediction results.

[0041] Figure 17 This is a graph showing the accuracy analysis of the permeability prediction results based on the Timur-Coates model in Experiment Example 1.

[0042] Figure 18 This is a graph showing the accuracy analysis of the permeability prediction results based on the SDR model in Experiment Example 1.

[0043] Figure 19 This is a graph showing the accuracy analysis of the permeability prediction results based on the Prince-Rezaee model in Experiment Example 1.

[0044] Figure 20 This is a graph showing the accuracy analysis of the permeability prediction results based on the Timur-Coates classification model in Experiment Example 1.

[0045] Figure 21 This is a graph showing the accuracy analysis of the permeability prediction results based on the SDR fractal model in Experiment Example 1.

[0046] Figure 22 This is a fluid distribution diagram of the sample before and after centrifugation in Experiment Example 2.

[0047] Figure 23 The graph shows the contribution of permeability measured by high-pressure mercury intrusion in Experiment Example 2. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0049] The abbreviations and key terms of this invention are defined as follows:

[0050] Abbreviations and key terms: pore size distribution, dense sandstone, pore structure, nuclear magnetic resonance, high pressure mercury intrusion, fractal analysis, mobile fluid and mobile fluid saturation, lower limit of mobile fluid pore size.

[0051] Definitions of abbreviations and key terms:

[0052] Pore ​​size distribution refers to the percentage of pores of various sizes present in a material, calculated by quantity or volume. Generally, mercury intrusion porosimetry and nuclear magnetic resonance (NMR) are used to test the pore size distribution of samples. The principle is to characterize the pore size distribution of the material by measuring the amount of mercury entering at the tested partial pressure and the relaxation signals of the corresponding pore sizes. The characterization method is to characterize the pore size distribution of the material by plotting the relationship between the volume of each pore size and the amount of mercury entering at the corresponding partial pressure.

[0053] Tight sandstone: a special type of sandstone composed of relatively dense clastic rocks, mainly including siltstone, fine sandstone, and some medium- to coarse sandstone; tight sandstone generally has a porosity of 7%-12% and a porosity of less than 1.0 × 10⁻⁶. -3 μm 2 The air permeability of sandstone is such that the pore radius is generally less than 0.5 μm.

[0054] Pore ​​structure refers to the type, size, distribution, and interconnections of pores and throats within a rock. A rock's pore system consists of two parts: pores and throats. Pores are the expanded parts of the system, while throats are the smaller parts connecting the pores. Pores are the basic storage spaces for fluids within rocks, while throats are important channels controlling fluid seepage. When fluids flow through the complex pore systems of nature, they pass through a series of alternating pores and throats.

[0055] Nuclear magnetic resonance (NMR) refers to the physical process by which the spin energy levels of atomic nuclei with non-zero magnetic moments undergo Zeeman splitting and resonant absorption of radio frequency radiation at a certain frequency under the influence of an external magnetic field. NMR has been widely used in the field of petroleum exploration and development. The T² distribution of NMR is directly related to the pore structure, thus enabling the acquisition of capillary pressure information. Compared with traditional capillary pressure measurements, NMR measurements are faster, more economical, non-destructive, and can be performed on a large scale.

[0056] High-pressure mercury intrusion porosimetry (HPMI) is a technique used to determine the pore size and distribution within a reservoir. HPMI relies on applied pressure to force mercury into the pores, overcoming surface tension, to determine pore size and distribution. Increasing the applied pressure allows mercury to enter smaller pores, resulting in a greater amount of mercury entering the pores. When assuming cylindrical pores, the pore size can be calculated based on the principle of balance between the surface tension of mercury in the pores and the applied pressure. HPMI requires that the mercury used be free of chemical impurities and physical contamination, as mercury contamination severely affects its surface tension and contact angle with the pores.

[0057] Centrifugation experiment: This refers to an experiment that uses centrifugal force to separate the components of a liquid and solid particles or a mixture of liquids. Centrifugation can be used to remove liquid from saturated water pores.

[0058] Fractal analysis refers to the morphological characteristics of fractals, which fill space with non-integer dimensions. It is typically defined as "a coarse or fragmented geometry that can be divided into several parts, each of which is (at least approximately) a scaled-down version of the whole," exhibiting self-similarity. Pore space within reservoirs is considered to possess self-similarity, and the complexity and heterogeneity of the pore structure can be quantitatively determined using fractal dimension.

[0059] Movable fluid and movable fluid saturation: Movable fluid is a fluid that can flow freely in pores under the action of external forces; movable fluid saturation describes the volume percentage of movable fluid in the pores of reservoir rocks, and this parameter affects the size of oil and gas reservoir reserves. Movable fluid saturation, along with porosity and permeability, is known as the porosity-permeability-saturation parameter, used to evaluate the quality of reservoirs.

[0060] Lower limit of movable fluid pore diameter: refers to the minimum pore radius that allows fluid flow in the reservoir pore structure under the action of external forces.

[0061] The permeability of tight sandstone has always been crucial for reservoir quality evaluation and classification; permeability is the most critical factor directly reflecting the permeability of tight sandstone reservoirs and ultimately determining their productivity. Due to the complex pore structure and strong heterogeneity of tight sandstone reservoirs, their permeability varies widely and is difficult to predict, necessitating the development of a permeability prediction model suitable for tight sandstone. In view of the problems with traditional techniques, this invention establishes a new model to obtain more accurate permeability data for tight sandstone.

[0062] One embodiment of the present invention provides a method for predicting the permeability of sandstone suitable for dense sandstone, such as... Figure 1 As shown, the method includes:

[0063] Step S1: Obtain either a first permeability prediction model or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution within the range of >40ms.

[0064] Step S2: Obtain the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample or the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40ms;

[0065] Step S3: Obtain the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size or the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample;

[0066] Step S4: Obtain the lower limit of the pore size of the movable fluid storage space of the target sample;

[0067] Step S5: Based on the cumulative mercury saturation distribution of the high-pressure mercury injection pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, determine the fractal dimension of the movable fluid storage space of the target sample, which is the first fractal dimension of the target sample; or; based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, determine the fractal dimension of the movable fluid storage space of the target sample, which is the second fractal dimension of the target sample;

[0068] Step S6: Based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, determine the permeability of the target sample using a first permeability prediction model based on fractal theory; or: Based on the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40ms and the second fractal dimension of the target sample, determine the permeability of the target sample using a second permeability prediction model based on fractal theory.

[0069] Furthermore, the first penetration rate prediction model based on fractal theory is as follows:

[0070]

[0071] In the formula, D m r is the fractal dimension of the movable fluid storage space, with a dimensionless unit. 20 The pore radius corresponding to a cumulative mercury saturation of 20% is expressed in μm; K is the permeability expressed in mD; a1, b1, and c1 are coefficients that can be obtained by fitting historical data. In a specific embodiment, a1 = 0.02, b1 = 2.23, and c1 = 1.63.

[0072] Furthermore, the second permeability prediction model based on fractal theory is as follows:

[0073]

[0074] In the formula, D m The fractal dimension of the movable fluid storage space, with dimensionless units; (T) 2gm ) >40 is the geometric mean of the transverse relaxation time > 40 ms in the T2 distribution of nuclear magnetic resonance, in ms; K is the permeability, in mD; a2, b2, and c2 are coefficients that can be obtained by fitting historical data. In a specific embodiment, a2 = 2.18 × 10 -8 b2 = 0.74, c2 = 2.51.

[0075] Furthermore, obtaining the pore radius corresponding to 20% cumulative mercury saturation of the target sample or the geometric mean of the transverse relaxation time >40ms in the NMR T2 distribution of the target sample can be done in a conventional manner; usually, the pore radius corresponding to 20% cumulative mercury saturation is determined based on the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size, which is obtained through high-pressure mercury intrusion analysis; the geometric mean of the transverse relaxation time >40ms in the NMR T2 spectrum is determined based on the NMR T2 distribution, which is determined through NMR analysis.

[0076] In one specific embodiment, the geometric mean of the transverse relaxation time in the T2 NMR spectrum within the range >40 ms is determined using the following formula:

[0077]

[0078] In the formula, (T) 2gm ) ＞40 The geometric mean of the values ​​within the range T2 > 40 ms, in milliseconds; Φ n The volume percentage at T2 = n ms (i.e., the porosity component at T2 = n ms), in %; Φ >40 Cumulative porosity within the range of T2 > 40 ms, in percentage.

[0079] Furthermore, the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size and the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample can be obtained in the conventional manner; usually, the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size is obtained through high-pressure mercury intrusion analysis; usually, the cumulative percentage distribution of the nuclear magnetic resonance pore size is determined based on the nuclear magnetic resonance T2 spectrum, which is determined through nuclear magnetic resonance analysis.

[0080] In one specific embodiment, when obtaining the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample, the transverse relaxation time T2 in the nuclear magnetic resonance T2 distribution of the target sample is converted into pore radius using the following formula;

[0081]

[0082] In the formula, T2 is the transverse relaxation time in ms; r is the pore radius in μm; m1 and n1 are conversion coefficients.

[0083] The conversion coefficients m1 and n1 can be determined in the following way:

[0084] The high-pressure mercury injection pore size distribution curve of the target sample was inversely accumulated and normalized with the nuclear magnetic resonance T2 spectrum to establish a distribution curve with the percentage of accumulation normalization as the abscissa and the transverse relaxation time T2 and pore radius r as the ordinate.

[0085] Obtain the transverse relaxation time T2 and pore radius r corresponding to several percentages, denoted as T 2(i) and r (i) ;

[0086] T 2(i) and r (i) Substituting into the formula lgT2=lgm1+n1lgr, and through multivariate linear fitting, the transformation coefficients m1 and n1 can be obtained.

[0087] Furthermore, the lower limit of the pore size of the movable fluid storage space of the target sample includes:

[0088] Determine the optimal centrifugal force for the target sample; wherein, the optimal centrifugal force is the minimum centrifugal force required to displace all movable fluid from the target sample through a centrifugation experiment;

[0089] The pore radius corresponding to the optimal centrifugal force of the target sample is determined as the lower limit of the pore size of the movable fluid storage space of the target sample;

[0090] Furthermore, the optimal centrifugal force for the target sample was determined in the following manner:

[0091] The T2 spectrum of a saturated water target sample was measured using nuclear magnetic resonance (NMR) experiments.

[0092] The target sample was centrifuged at different speeds, with the speed gradually increasing.

[0093] After each centrifugation, the T2 spectrum of the target sample was measured;

[0094] When the T2 spectrum amplitude does not change after a certain centrifugation or the saturation of the mobile fluid decreases by less than 5%, the centrifugation speed at this time is the optimal centrifugation speed, and the centrifugation force corresponding to the optimal centrifugation speed is the optimal centrifugation force; the optimal centrifugation force can be determined according to the following formula;

[0095]

[0096] In the formula, RCF is the centrifugal force, in g; r is the pore radius of the centrifuged sample, in mm; rpm is the rotational speed, in rpm;

[0097] Furthermore, the pore radius corresponding to the optimal centrifugal force of the target sample is determined according to the Washburn equation;

[0098] The Washburn equation is as follows:

[0099] In the formula, P c σ is the capillary pressure in MPa; σ is the mercury surface tension in mN / m; θ is the contact angle; r is the pore radius in nm. Under gas-water conditions, when σ is 72.75 mN / m and θ is 0°, the capillary pressure is the centrifugal force.

[0100] Furthermore, based on the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the first fractal dimension of the target sample, including:

[0101] Take data points from the cumulative mercury saturation distribution of high-pressure mercury intrusion pore size of the target sample, where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space;

[0102] Based on the pore radius and cumulative mercury saturation value corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula:

[0103] lg(1-S Hg )=(3-D m )lgr-(3-D m )lgr max

[0104] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; Hg The cumulative mercury saturation is expressed as a percentage (%); r is the pore radius, expressed as μm. max This represents the maximum pore radius.

[0105] Furthermore, based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the second fractal dimension of the target sample, including:

[0106] Take data points from the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space;

[0107] Based on the pore radius and cumulative volume percentage corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula:

[0108] lg(S w )=(3-D m )lgr-(3-D m )lgr max

[0109] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; w The cumulative volume percentage is %; r is the pore radius in μm. max This represents the maximum pore radius.

[0110] An embodiment of the present invention provides a sandstone permeability prediction system suitable for dense sandstone. This system can implement the sandstone permeability prediction method provided in the above embodiment. The system includes:

[0111] Model acquisition module 21: used to acquire either a first permeability prediction model based on fractal theory or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution within the range of >40ms.

[0112] First data acquisition module 22: used to acquire the pore radius corresponding to a cumulative mercury saturation of 20% of the target sample or the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution of the target sample within the range of >40ms;

[0113] Second data acquisition module 23: used to acquire the cumulative mercury saturation distribution of high-pressure mercury injection pore size or the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample;

[0114] Module 24 for determining the lower limit of the pore size: used to obtain the lower limit of the movable fluid storage space of the target sample;

[0115] Fractal dimension determination module 25: Based on the cumulative mercury saturation distribution of the high-pressure mercury injection pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the first fractal dimension of the target sample; or; based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the second fractal dimension of the target sample.

[0116] Permeability determination module 26: Used to determine the permeability of the target sample based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, using a first permeability prediction model based on fractal theory; or; based on the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40ms and the second fractal dimension of the target sample, using a second permeability prediction model based on fractal theory.

[0117] Furthermore, the first penetration rate prediction model based on fractal theory is as follows:

[0118]

[0119] In the formula, D m r is the fractal dimension of the movable fluid storage space, with a dimensionless unit. 20The pore radius corresponding to a cumulative mercury saturation of 20% is expressed in μm; K is the permeability expressed in mD; a1, b1, and c1 are coefficients that can be obtained by fitting historical data. In a specific embodiment, a1 = 0.02, b1 = 2.23, and c1 = 1.63.

[0120] Furthermore, the second permeability prediction model based on fractal theory is as follows:

[0121]

[0122] In the formula, D m The fractal dimension of the movable fluid storage space, with dimensionless units; (T) 2gm ) >40 is the geometric mean of the transverse relaxation time > 40 ms in the T2 distribution of nuclear magnetic resonance, in ms; K is the permeability, in mD; a2, b2, and c2 are coefficients that can be obtained by fitting historical data. In a specific embodiment, a2 = 2.18 × 10 -8 b2 = 0.74, c8 = 2.51.

[0123] Furthermore, when obtaining the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, the transverse relaxation time T2 in the nuclear magnetic resonance T2 distribution of the target sample is converted into the pore radius using the following formula;

[0124]

[0125] In the formula, T2 is the transverse relaxation time in ms; r is the pore radius in μm; m1 and n1 are conversion coefficients.

[0126] The conversion coefficients m1 and n1 can be determined in the following way:

[0127] The high-pressure mercury injection pore size distribution curve of the target sample was inversely accumulated and normalized with the nuclear magnetic resonance T2 spectrum to establish a distribution curve with the percentage of accumulation normalization as the abscissa and the transverse relaxation time T2 and pore radius r as the ordinate.

[0128] Obtain the transverse relaxation time T2 and pore radius r corresponding to several percentages, denoted as T 2(i) and r (i) ;

[0129] T 2(i) and r (i) Substituting into the formula lgT2=lgm1+n1lgr, and through multivariate linear fitting, the transformation coefficients m1 and n1 can be obtained.

[0130] Furthermore, the aperture lower limit determination module 24 includes:

[0131] Optimal centrifugal force determination submodule 241: used to determine the optimal centrifugal force for the target sample; wherein, the optimal centrifugal force is the minimum centrifugal force required for the target sample to expel all movable fluid through a centrifugation experiment;

[0132] Pore ​​diameter lower limit determination submodule 242: used to determine the pore radius corresponding to the optimal centrifugal force of the target sample as the pore diameter lower limit of the movable fluid storage space of the target sample.

[0133] Furthermore, the fractal dimension determination module 25 is specifically used for:

[0134] Take data points from the cumulative mercury saturation distribution of high-pressure mercury intrusion pore size of the target sample, where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space;

[0135] Based on the pore radius and cumulative mercury saturation value corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula:

[0136] lg(1-S Hg )=(3-D m )lgr-(3-D m )lgr max

[0137] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; Hg The cumulative mercury saturation is expressed as a percentage (%); r is the pore radius, expressed as μm. max This represents the maximum pore radius.

[0138] Furthermore, the fractal dimension determination module 25 is specifically used for:

[0139] Take data points from the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space;

[0140] Based on the pore radius and cumulative volume percentage corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula:

[0141] lg(S w )=(3-D m )lgr-(3-D m )lgr max

[0142] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; w The cumulative volume percentage is %; r is the pore radius in μm. maxThis represents the maximum pore radius.

[0143] This invention also provides a storage medium. The storage medium stores one or more programs. The storage medium may include volatile memory, such as random access memory; it may also include non-volatile memory, such as read-only memory, flash memory, hard disk, or solid-state drive; and it may also include combinations of the above types of memory.

[0144] When one or more programs in the storage medium can be executed by one or more processors to implement the steps of the above sandstone permeability prediction method, please refer to the above sandstone permeability prediction method embodiment for details, which will not be repeated here.

[0145] One embodiment of the present invention provides a sandstone permeability prediction device suitable for dense sandstone. The device includes: a processor communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus.

[0146] Memory, used to store computer programs;

[0147] When the processor executes the program stored in the memory to implement the steps of the above-described sandstone permeability prediction method, the specific steps of the method are detailed in the above-described sandstone permeability prediction method embodiment, and will not be repeated here.

[0148] Example 1

[0149] This embodiment uses the determination of the permeability of a certain tight sandstone as an example to illustrate the sandstone permeability prediction technology provided by the present invention. Specifically, this embodiment determines the permeability of the target tight sandstone using the following sandstone permeability prediction method:

[0150] 1. Obtain the first penetration rate prediction model based on fractal theory and the second penetration rate prediction model based on fractal theory; wherein,

[0151] The first penetration rate prediction model based on fractal theory is:

[0152] K = 0.02 × (D m ) 2.23 ×(r 20 ) 1.63

[0153] In the formula, D m r is the fractal dimension of the movable fluid storage space, with a dimensionless unit. 20 The pore radius corresponds to a cumulative mercury saturation of 20%, in μm; K is the permeability, in mD.

[0154] The second permeability prediction model based on fractal theory is as follows:

[0155] K = 2.18 × 10 -8 ×(D m ) 0.74 ×((T 2gm ) >40 ) 2.51

[0156] In the formula, D m The fractal dimension of the movable fluid storage space, with dimensionless units; (T) 2gm ) >40 is the geometric mean of the transverse relaxation time in the T2 distribution of nuclear magnetic resonance within the range of >40ms, in ms; K is the permeability, in mD.

[0157] 2. Take a target reservoir sample as the target sample and perform high-pressure mercury intrusion porosimetry (HPMI) to determine the HPMI pore size distribution curve and the cumulative mercury saturation distribution curve of the HPMI pore size (e.g., Figure 2 (as shown), and determine the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample (e.g. Figure 3 As shown), denoted as r 20 .

[0158] 3. Take the target sample for nuclear magnetic resonance (NMR) analysis and obtain the NMR echo train of the target sample. Perform multi-exponential inversion (singular value decomposition algorithm) on the NMR relaxation signal to determine the NMR T2 spectrum and cumulative percentage curve (e.g., Figure 4 The geometric mean of the transverse relaxation time T2 > 40 ms in the nuclear magnetic resonance T2 distribution is determined using the following formula, denoted as (T 2gm ) >40 :

[0159]

[0160] In the formula, (T) 2gm ) >40 The geometric mean of the values ​​within the range T2 > 40 ms, in milliseconds; Φ n The volume percentage at T2 = n ms (i.e., the porosity component at T2 = n ms), in %; Φ >40 Cumulative porosity within the range of T2 > 40 ms, in percentage.

[0161] The high-pressure mercury intrusion pore size distribution curve and the nuclear magnetic resonance T2 spectrum of the target sample were inversely accumulated and normalized to establish a distribution curve with the percentage of accumulated normalization as the abscissa and T2 and pore radius r as the ordinate (e.g. Figure 5 As shown in the figure, a straight line parallel to the vertical axis is randomly selected. This line intersects the inverse cumulative normalization curve of the T2 spectrum and the inverse cumulative normalization curve of the high-pressure mercury injection pore size distribution, respectively. The corresponding values ​​are denoted as T.2(i) and r (i) In this way, a number of one-to-one corresponding Ts can be obtained. 2(i) and r (i) .

[0162] T 2(i) and r (i) Substituting into the formula lgT2=lgm1+n1lgr, and through multiple linear fitting, the transformation coefficients m1=693.72 and n1=1.52 can be obtained; then using the formula The transverse relaxation time T2 in the NMR T2 spectrum of the target sample was converted into pore radius, thereby determining the cumulative percentage distribution of the NMR pore size of the target sample. The results are as follows: Figure 6 As shown.

[0163] 4. Perform nuclear magnetic resonance (NMR) experiments on the saturated water target sample to measure the T2 spectrum. Centrifuge the target sample at 2000 rpm, 3500 rpm, 5000 rpm, 7500 rpm, 10000 rpm, 12500 rpm, and 15000 rpm respectively. Measure the T2 spectrum of the target sample after each centrifugation. Figure 7 As shown, when the centrifuge speed increased from 12,500 rpm to 15,000 rpm, less than 2.4% of mobile water was centrifuged out, and the T2 spectrum showed almost no change. The optimal centrifugation speed for the target sample was determined to be 15,000 rpm, and the optimal centrifugal force was determined to be 23,897.25 × g (i.e., 8.53 MPa) using the following formula:

[0164]

[0165] In the formula, RCF is the centrifugal force, in g; r is the pore radius of the centrifuged sample, in mm; rpm is the rotational speed, in rpm;

[0166] The pore radius corresponding to the optimal centrifugal force is determined by the following formula and used as the lower limit r of the pore size of the movable fluid storage space of the target sample. cutoff :

[0167] 5. Take data points from the cumulative mercury saturation distribution of the high-pressure mercury injection pore size of the target sample, where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; based on the pore radius and cumulative mercury saturation value corresponding to the selected data points, perform fitting according to the following formula (e.g. Figure 8 As shown), the fractal dimension of the movable fluid storage space of the target sample is the first fractal dimension of the target sample:

[0168] lg(1-S Hg )=(3-D m )lgr-(3-D m )lgr max

[0169] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; Hg The cumulative mercury saturation is expressed as a percentage (%); r is the pore radius, expressed as μm. max The maximum pore radius;

[0170] For comparison, data points with pore radii smaller than the lower limit of the movable fluid storage space in the cumulative mercury intrusion saturation distribution of the high-pressure mercury intrusion pore size of the target sample were selected. Based on the pore radius and cumulative mercury intrusion saturation value corresponding to the selected data points, a fitting was performed according to the above formula, and the results are as follows. Figure 8 As shown;

[0171] Take data points from the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; based on the pore radius and cumulative volume percentage values ​​corresponding to the selected data points, perform fitting according to the following formula (e.g.) Figure 9 As shown), the fractal dimension of the movable fluid storage space of the target sample is the second fractal dimension of the target sample:

[0172] lg(S w )=(3-D m )lgr-(3-D m )lgr max

[0173] In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; w The cumulative volume percentage is %; r is the pore radius in μm. max The maximum pore radius;

[0174] For comparison, data points in the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample where the pore radius is smaller than the lower limit of the movable fluid storage space were selected. Based on the pore radius and cumulative mercury saturation value corresponding to the selected data points, a fitting was performed according to the above formula, and the results are as follows. Figure 9 As shown.

[0175] 6. Based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, the permeability of the target sample is determined using the first permeability prediction model based on fractal theory.

[0176] Based on the geometric mean of the transverse relaxation time > 40 ms in the nuclear magnetic resonance T2 distribution of the target sample and the second fractal dimension of the target sample, the permeability of the target sample is determined using a second permeability prediction model based on fractal theory.

[0177] Experimental Example 1

[0178] This experimental example is used to evaluate the accuracy of the sandstone permeability prediction method provided by the present invention.

[0179] Currently, commonly used metrics for evaluating the accuracy of prediction models include: MSE (mean squared error), RMSE (root mean squared error), MAPE (mean absolute percentage error), and MAE (mean absolute error); among these, RMSE and MAPE are the most widely used. RMSE reflects the deviation between the predicted and actual values; while MAPE represents the mean absolute percentage error. Because penetration rates vary widely (spanning orders of magnitude), to better evaluate the accuracy of penetration rate prediction models, both the root mean squared error (absolute value) and the mean absolute percentage error (relative value) must be considered. Therefore, RMSE and MAPE are used as error metrics to evaluate the accuracy of prediction models. RMSE and MAPE are normalized to calculate the Accuracy Index (ACI). A higher ACI indicates higher prediction accuracy of the penetration rate prediction model.

[0180] Root mean square error:

[0181] Mean absolute percentage error:

[0182] Normalization:

[0183]

[0184] In the formula, K is the experimentally measured permeability, in mD; K * To predict penetration rate, mD; E r E represents the sum of the inverse errors of the penetration rate prediction model. r min E is the minimum of 1 / MAPE and 1 / RMSE in the set. r max It is the minimum of 1 / MAPE and 1 / RMSE in the set.

[0185] Multiple target samples were obtained, and their permeability was predicted using the following permeability prediction model. The prediction accuracy was then determined.

[0186] (1) Permeability prediction model based on high-pressure mercury intrusion technology:

[0187] 1)r 10 Model, r 25 Model, r 35 Model

[0188] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0189] ② High-pressure mercury intrusion porosimetry: Obtain the pore radii corresponding to cumulative mercury saturation of 10%, 25%, and 35%, respectively, denoted as r. 10 r 25 r 35 ;

[0190] ③ Establishment of penetration rate prediction model:

[0191] r 10 Model:

[0192] r 25 Model:

[0193] r 35 Model:

[0194] In the formula: K is permeability, in mD; Ф is porosity, in %; r i The pore radius corresponding to the cumulative mercury saturation of i%, in μm; a n b n c n Let n be the coefficient, where n = 3, 4, 5;

[0195] ④ Taking the logarithm of both sides of the model equation, we get:

[0196] ⑤Use r respectively 10 Model, r 25 Model, r 35 The model combines gas-measured porosity with the pore radius r corresponding to cumulative mercury saturation of 10%, 25%, and 35%. 10 r 25 r 35 The permeability of each target sample was predicted, and the prediction accuracy was determined. The results are as follows: Figure 12 , Figure 13 , Figure 14 As shown.

[0197] 2) Swanson model

[0198] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0199] ② High-pressure mercury intrusion analysis: Obtain the maximum value of the ratio of mercury saturation to capillary pressure, which is the Swanson factor;

[0200] ③ Establishment of the penetration rate prediction model:

[0201] Swanson model:

[0202]

[0203] In the formula: K is the permeability, in mD; S Hg Cumulative mercury saturation, in %; P c ρ is capillary pressure, in MPa; m2 and n2 are coefficients; this model uses a factor (maximum value of mercury saturation / capillary pressure) to predict permeability;

[0204] ④ Taking the logarithm of both sides of the model equation, we get:

[0205] For lgK and lg(S) Hg / P c Perform multiple linear regression analysis to obtain the coefficients in the penetration rate prediction model;

[0206] ⑤ The permeability of each target sample was predicted using the Swanson model combined with gas porosity and the Swanson factor, and the prediction accuracy was determined accordingly. The results are as follows: Figure 15 As shown.

[0207] 3)r apex Model

[0208] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0209] ② High-pressure mercury intrusion porosimetry: Obtain the pore radius corresponding to the Swanson factor, denoted as r. apex ;

[0210] ③ Establishment of the penetration rate prediction model:

[0211] r apex Model:

[0212]

[0213] In the formula: K is permeability, in mD; Ф is porosity, in %; r apex The pore radius corresponding to the maximum value of mercury saturation / capillary pressure, in μm; a6, b6, and c6 are coefficients;

[0214] ④ Taking the logarithm of both sides of the model equation, we get:

[0215] For lgK, lgΦ and lgr apex Perform multiple linear regression analysis to obtain the coefficients in the penetration rate prediction model;

[0216] ⑤Use r respectively apex The model combines gas porosity and r apex The permeability of each target sample was predicted, and the prediction accuracy was determined. The results are as follows: Figure 16 As shown.

[0217] Among the five permeability prediction models based on high-pressure mercury intrusion porosimetry, the one with the highest prediction accuracy is r. apex The model with an ACI of 0.60 was the best, while the prediction results of the other models were not ideal.

[0218] (2) Permeability prediction model based on nuclear magnetic resonance technology:

[0219] 1) Timur-Coates model

[0220] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0221] ② Nuclear magnetic resonance analysis test: Obtain the ratio of the volume of movable fluid to the volume of bound fluid, denoted as FFI / BVI.

[0222] ③ Establishment of the penetration rate prediction model:

[0223] Timur-Coates model:

[0224]

[0225] In the formula: K is permeability, in mD; Ф is porosity, in %; FFI is free fluid volume, in cm³. 3 BVI stands for volume of immovable fluid, in cm³. 3 a7, b7, and c7 are coefficients.

[0226] ④ Taking the logarithm of both sides of the model equation, we get:

[0227] Multiple linear regression analysis was performed on lgK, lgΦ, and lg(FFI / BVI) to obtain the coefficients in the penetration rate prediction model;

[0228] ⑤ The permeability of each target sample was predicted using the Timur-Coates model combined with gas porosity and FFI / BVI, and the prediction accuracy was determined accordingly. The results are as follows: Figure 17 As shown.

[0229] 2) SDR model

[0230] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0231] ② Nuclear magnetic resonance analysis test: Obtain the geometric mean of the T2 spectrum, denoted as T. 2gm .

[0232] ③ Establishment of the penetration rate prediction model:

[0233] SDR model:

[0234]

[0235] Where: K is permeability, in mD; Ф is porosity, in %; T 2gm is the geometric mean of the transverse relaxation time, in milliseconds; a8, b8, and c8 are coefficients;

[0236] ④ Taking the logarithm of both sides of the model equation, we get:

[0237] For lgK, lgΦ and lg(T) 2gm Perform multiple linear regression analysis to obtain the coefficients in the penetration rate prediction model;

[0238] ⑤ Using the SDR model in combination with gas porosity and T 2gm The permeability of each target sample was predicted, and the prediction accuracy was determined. The results are as follows: Figure 18 As shown.

[0239] 3) Prince-Rezaee model

[0240] ① Physical property analysis and testing: Obtain gas porosity and Kjeldahl permeability;

[0241] ② Nuclear magnetic resonance analysis and testing: Obtain the relaxation time of the spectral peak (the relaxation time corresponding to the maximum porosity component), denoted as T. 2v .

[0242] ③ Establishment of the penetration rate prediction model:

[0243] Prince-Rezaee model:

[0244] K = -a9 - b9 × Φ - c9 × T 2v

[0245] Where: K is permeability, in mD; Ф is porosity, in %; T 2v is the transverse relaxation time of the spectral peak, in milliseconds; a9, b9, and c9 are coefficients.

[0246] ④ Regarding K, Φ and T 2gv Perform multiple linear regression analysis to obtain the coefficients in the penetration rate prediction model;

[0247] ⑤ Using the Prince-Rezaee model in conjunction with gas porosity and T, respectively 2v The permeability of each target sample was predicted, and the prediction accuracy was determined. The results are as follows: Figure 19 As shown.

[0248] The three permeability prediction models based on nuclear magnetic resonance technology did not perform well. The Timur-Coates model and the SDR model had relatively high prediction accuracy (ACI of only 0.50), while the Prince-Rezaee model had the lowest (ACI of 0.44).

[0249] (3) Permeability prediction model based on fractal dimension:

[0250] 1) Physical property analysis and testing: obtain gas porosity and Kjeldahl permeability.

[0251] 2) Fractal Analysis

[0252] ① Nuclear magnetic resonance analysis test

[0253] Obtain the ratio of the T2 spectrum to the volume of movable fluid to the volume of bound fluid (FFI / BVI), and the geometric mean of the T2 spectrum (T). 2gm ), T2 cutoff value (T) 2cutoff );

[0254] ② Create a fractal scatter plot

[0255] The fractal model is represented as:

[0256]

[0257] In the formula, T2 is the transverse relaxation time of the rock sample's nuclear magnetic resonance, in milliseconds; T 2max The maximum transverse relaxation time of the rock sample via nuclear magnetic resonance (NMR) is expressed in milliseconds (ms). w The cumulative percentage of transverse relaxation times less than T2 in nuclear magnetic resonance (i.e., the cumulative porosity component of transverse relaxation times less than T2 in nuclear magnetic resonance), %;

[0258] Taking the logarithm of both sides of the fractal model, we get: lgS w = (3-D)lgT2-(3-D)lgT 2max

[0259] Construct lgT2 as the x-axis and lgS w A fractal scatter plot with the vertical axis as the ordinate;

[0260] ③ Obtain the fractal dimension of the macropore

[0261] Aperture larger than T 2cutoff The pore size is macropore; the pore diameter is smaller than T. 2cutoff The value is for the small hole; when performing fractal segmentation analysis, T is used. 2cutoff The logarithm of the value is used as the boundary point of different fractal segments. A linear fit is performed on the scatter points to the right of the segment point. The fractal dimension of the macropore is obtained by the slope of the linear relationship (3-D) obtained through the fitted curve. b ) is obtained, denoted as Db .

[0262] 3) Establishment of a penetration rate prediction model

[0263] ① Timur-Coates typing model:

[0264] SDR fractal model:

[0265] Where: K is permeability, in mD; Ф is porosity, in %; T 2gm FFI is the geometric mean of the transverse relaxation time, in milliseconds (ms); FFI is the free fluid volume, in centimeters (cm³). 3 BVI stands for volume of immovable fluid, in cm³. 3 ;a 10 b 10 c 10 a 11 b 11 c 11 D is the coefficient; b It is the fractal dimension;

[0266] ② Taking the logarithm of both sides of the model, we get:

[0267]

[0268]

[0269] For lgK, lgΦ, D b lgΦ is related to lg(FFI / BVI) and lg(T) respectively. 2gm Perform multiple linear regression analysis to obtain the coefficients in the penetration rate prediction model;

[0270] 4) Using the Timur-Coates fractal model and the SDR fractal model respectively, combined with gas porosity, FFI / BVI, and T 2gm The permeability of each target sample was predicted, and the prediction accuracy was determined. The results are as follows: Figure 20 , Figure 21 As shown.

[0271] The two permeability prediction models based on fractal dimension did not perform well, with the Timur-Coates fractal model and the SDR fractal model having ACI values ​​of only 0.05 and 0.10, respectively.

[0272] Multiple target samples were obtained, and permeability prediction was performed using the sandstone permeability prediction method described in the example. Permeability prediction results based on the first permeability prediction model and the second permeability prediction model were obtained. The permeability of each target sample was determined through Kjeldahl permeability analysis. Furthermore, accuracy analyses were performed on the permeability prediction results based on the first and second permeability prediction models. The results are as follows: Figure 10 , Figure 11 As shown.

[0273] Compared with previous penetration rate prediction models, the penetration rate prediction model provided in this invention has higher accuracy: the ACI of the first penetration rate prediction model is 0.85, which is the highest among all prediction models (compared to r). apex Compared to the first model, the prediction accuracy was improved by 42%; the ACI of the second penetration rate prediction model was 0.72, and its prediction accuracy was second only to the first penetration rate prediction model (compared to r). apex Compared to the previous model, the prediction accuracy has improved by 20%.

[0274] Experiment Example 2

[0275] This experimental example is used to verify the effectiveness of determining the fractal dimension by using the pore radius corresponding to the optimal centrifugal force as the lower limit of the pore size, compared to using nuclear magnetic resonance T... 2cutoff Using the pore radius corresponding to the value as the lower limit of the pore diameter for fractal dimension determination is more accurate.

[0276] Taking a certain sample as an example, the nuclear magnetic resonance T of this sample 2cutoff The pore radius corresponding to the optimal centrifugal force is 33 nm; while the pore radius corresponding to the optimal centrifugal force is 17.05 nm. The fluid distribution before and after centrifugation is as follows: Figure 22 As shown: Compared to 33 nm, the 17.05 nm line better characterizes the lower limit of mobile fluid, with more mobile fluid to the right of the 17.05 nm line (reaching 96%). In comparison, NMR T... 2cutoff The value neglects the contribution of some small pores to seepage (e.g. Figure 23 As shown in the figure, this has a certain impact on the accuracy of the permeability model.

Claims

1. A method for predicting sandstone permeability, wherein, The method includes: Obtain either a first permeability prediction model or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; and the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution range >40 ms. Obtain the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample, or the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40 ms; Obtain the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size or the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample; To obtain the lower limit of the pore size of the movable fluid storage space of the target sample; Based on the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size of the target sample, the lower limit of the pore size of the movable fluid storage space is used as the boundary point for fractal analysis, and the fractal dimension of the movable fluid storage space of the target sample is determined as the first fractal dimension of the target sample; or, based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, the lower limit of the pore size of the movable fluid storage space is used as the boundary point for fractal analysis, and the fractal dimension of the movable fluid storage space of the target sample is determined as the second fractal dimension of the target sample. Based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, the permeability of the target sample is determined using a first permeability prediction model based on fractal theory; or, based on the geometric mean of the transverse relaxation time in the T2 distribution of the nuclear magnetic resonance of the target sample within the range of >40 ms and the second fractal dimension of the target sample, the permeability of the target sample is determined using a second permeability prediction model based on fractal theory. The first penetration rate prediction model based on fractal theory is as follows: In the formula, D m r is the fractal dimension of the movable fluid storage space, with a dimensionless unit. 20 The pore radius corresponding to a cumulative mercury saturation of 20% is expressed in μm; K is the permeability, expressed in mD; a1, b1, and c1 are coefficients. The second permeability prediction model based on fractal theory is as follows: In the formula, D m The fractal dimension of the movable fluid storage space is dimensionless. is the geometric mean of the transverse relaxation time in the T2 distribution of nuclear magnetic resonance within the range of >40 ms, in ms; K is the permeability, in mD; a2, b2, and c2 are coefficients.

2. The method according to claim 1, wherein, a1=0.02, b1=2.23, c1=1.63; and / or a2 = 2.18 × 10 -8 b2=0.74, c2=2.

51.

3. The method according to claim 1, wherein, The lower limit of the pore size of the movable fluid storage space of the target sample includes: Determine the optimal centrifugal force for the target sample; wherein, the optimal centrifugal force is the minimum centrifugal force required to displace all movable fluid from the target sample through a centrifugation experiment; The pore radius corresponding to the optimal centrifugal force of the target sample is determined as the lower limit of the pore size of the movable fluid storage space of the target sample.

4. The method according to claim 1, wherein, Based on the cumulative mercury saturation distribution of the high-pressure mercury intrusion pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the first fractal dimension of the target sample, including: Take data points from the cumulative mercury saturation distribution of high-pressure mercury intrusion pore size of the target sample, where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; Based on the pore radius and cumulative mercury saturation value corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula: In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; Hg The cumulative mercury saturation is expressed as %; r is the pore radius, expressed as μm. max The maximum pore radius; Based on the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample, and using the lower limit of the pore size of the movable fluid storage space as the boundary point for fractal analysis, the fractal dimension of the movable fluid storage space of the target sample is determined, which is the second fractal dimension of the target sample, including: Take data points from the cumulative percentage distribution of nuclear magnetic resonance pore size of the target sample where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; Based on the pore radius and cumulative volume percentage corresponding to the data points, the fractal dimension of the movable fluid storage space of the target sample is obtained by fitting according to the following formula: In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; w The value is a cumulative volume percentage (%), and r is the pore radius (μm). max This represents the maximum pore radius.

5. A sandstone permeability prediction system, wherein, The system includes: Model acquisition module: used to acquire either a first permeability prediction model or a second permeability prediction model based on fractal theory; wherein, the first permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the pore radius corresponding to a cumulative mercury saturation of 20%; the second permeability prediction model based on fractal theory is a calculation model of permeability with respect to the fractal dimension of the movable fluid storage space and the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution range >40 ms; First data acquisition module: used to acquire the pore radius corresponding to a cumulative mercury saturation of 20% for the target sample or the geometric mean of the transverse relaxation time in the nuclear magnetic resonance T2 distribution of the target sample within the range of >40 ms; The second data acquisition module is used to acquire the cumulative mercury saturation distribution of the high-pressure mercury injection pore size or the cumulative percentage distribution of the nuclear magnetic resonance pore size of the target sample. Pore ​​diameter lower limit determination module: used to obtain the lower limit of the pore diameter of the movable fluid storage space of the target sample; The fractal dimension determination module is used to determine the first fractal dimension of the target sample's movable fluid storage space based on the cumulative mercury saturation distribution of the high-pressure mercury injection pore size, using the lower limit of the movable fluid storage space's pore size as the boundary point for fractal analysis; or, based on the cumulative percentage distribution of the target sample's nuclear magnetic resonance pore size, using the lower limit of the movable fluid storage space's pore size as the boundary point for fractal analysis, the second fractal dimension of the target sample's movable fluid storage space is determined. The permeability determination module is used to determine the permeability of a target sample based on the pore radius corresponding to a cumulative mercury saturation of 20% and the first fractal dimension of the target sample, using a first permeability prediction model based on fractal theory; or, based on the geometric mean of the transverse relaxation time in the T2 distribution of the target sample's nuclear magnetic resonance within the range of >40 ms and the second fractal dimension of the target sample, using a second permeability prediction model based on fractal theory. The first penetration rate prediction model based on fractal theory is as follows: In the formula, D m r is the fractal dimension of the movable fluid storage space, with a dimensionless unit. 20 The pore radius corresponding to a cumulative mercury saturation of 20% is expressed in μm; K is the permeability, expressed in mD; a1, b1, and c1 are coefficients. The second permeability prediction model based on fractal theory is as follows: In the formula, D m The fractal dimension of the movable fluid storage space is dimensionless. is the geometric mean of the transverse relaxation time in the T2 distribution of nuclear magnetic resonance within the range of >40 ms, in ms; K is the permeability, in mD; a2, b2, and c2 are coefficients.

6. The system according to claim 5, wherein, a1=0.02, b1=2.23, c1=1.63; and / or a2 = 2.18 × 10 -8 b2=0.74, c2=2.

51.

7. The system according to claim 5, wherein, The aperture lower limit determination module includes: Optimal centrifugal force determination submodule: used to determine the optimal centrifugal force for the target sample; wherein, the optimal centrifugal force is the minimum centrifugal force required for the target sample to expel all movable fluid through a centrifugation experiment; The lower limit pore size determination submodule is used to determine the pore radius corresponding to the optimal centrifugal force of the target sample as the lower limit of the pore size of the movable fluid storage space of the target sample.

8. The system according to claim 5, wherein, The fractal dimension determination module is used to: extract data points from the cumulative mercury saturation distribution of the high-pressure mercury injection pore size of the target sample, where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; and, based on the pore radius and cumulative mercury saturation value corresponding to the extracted data points, fit the data using the following formula to obtain the fractal dimension of the movable fluid storage space of the target sample: In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; Hg The cumulative mercury saturation is expressed as %; r is the pore radius, expressed as μm. max The maximum pore radius; The fractal dimension determination module is used to: extract data points from the cumulative percentage distribution of nuclear magnetic resonance pore sizes of the target sample where the pore radius is not less than the lower limit of the pore size of the movable fluid storage space; and, based on the pore radius and cumulative volume percentage values ​​corresponding to the extracted data points, fit the data using the following formula to obtain the fractal dimension of the movable fluid storage space of the target sample: In the formula, D m S is the fractal dimension of the movable fluid storage space, with dimensionless units; w The value is a cumulative volume percentage (%), and r is the pore radius (μm). max This represents the maximum pore radius.

9. A storage medium, wherein, The storage medium stores one or more programs, which can be executed by one or more processors to implement the sandstone permeability prediction method according to any one of claims 1-4.

10. A device for predicting and determining the permeability of sandstone, the device comprising: The processor communication interface, memory, and communication bus are used to communicate with each other. Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the sandstone permeability prediction method according to any one of claims 1-4.

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