A method for calculating thermal conductivity of quartz sandstone using crystal structure

Abstract

This invention relates to a method for calculating the thermal conductivity of quartz sandstone using its crystal structure. The method involves measuring the density of the quartz sandstone using Archimedes' buoyancy method, testing the true density of the quartz sandstone sample using nitrogen as the buoyancy medium, determining the apparent relative density of the quartz sandstone using a volumetric flask method, and calculating the porosity of the quartz sandstone. XRD is used to obtain mineral content data and 2θ angle and peak intensity data in the quartz sandstone. The weight percentage of mineral components is converted to volume percentage. Quartz crystal structure parameters are used to correct the thermal conductivity value of the quartz sandstone. The Scherrer formula is used to calculate the quartz grain size as a grain correction coefficient for calculating the thermal conductivity of the quartz sandstone. Quartz crystallinity is used as a macroscopic crystallinity correction coefficient for the thermal conductivity of the quartz sandstone. Finally, the thermal conductivity of the quartz sandstone is calculated. This invention solves the problem of being unable to measure thermal conductivity due to the inability to drill complete samples.

Description

Technical Field

[0001] This invention relates to the technical field of calculating the thermal conductivity of quartz sandstone, and in particular to a method for calculating the thermal conductivity of quartz sandstone using crystal structure. Background Technology

[0002] In geothermal resource development, mineral resource extraction, and building insulation assessment, accurate calculation of sandstone thermal properties such as thermal conductivity and thermal diffusivity can effectively reduce project budgets and decrease construction risks and failure rates. Simultaneously, it holds significant scientific importance for research on lithospheric geothermal processes, terrestrial heat flow, and rock conduction. Thermal conductivity determines the heat transfer efficiency and insulation performance of rocks, making it the most important parameter in rock thermodynamics. However, in traditional scientific research and engineering construction, rock thermal conductivity data is often obtained through laboratory sample measurements. This method has limitations for large-scale sample studies and data acquisition, requiring numerous experimental samples and considerable testing time, severely restricting research and development related to rock thermal conductivity. This is particularly true for rock cuttings samples generated during oil and gas drilling, where existing experimental instruments struggle to perform laboratory measurements of thermal conductivity in fragmented samples. Quartz sandstone is a special type of sedimentary rock, formed after weathering and subsequent long-term sorting and rounding processes. It is abundant in platform regions within marine environments and is a crucial component of sedimentary strata. The most important characteristic of quartz sandstone is that its main component is quartz clasts, which have a relatively stable and homogeneous composition. At the same time, compared to other clastic minerals (such as feldspar, mica, dolomite, and clay minerals), quartz has a much higher thermal conductivity than other clastic particles. Therefore, the thermal conductivity of quartz sandstone is mainly controlled by quartz.

[0003] Currently, the main method for obtaining the thermal conductivity of rocks is through laboratory measurements, primarily using transient plane sources, optical scanning methods, and other testing methods and instruments to test the thermal conductivity of quartz sandstone samples. When it is difficult to obtain suitable rock samples for laboratory measurements of the thermal conductivity of quartz sandstone, a common method is to predict the thermal conductivity value of quartz sandstone using mineralogical data of the constituent rocks. Common calculation models include geometric mean, harmonic mean, square root mean, and HS mean. However, the calculated results often differ significantly from the actual results, and the above methods mainly consider mineral content, especially quartz content, but do not account for the structural variations of quartz, which leads to large discrepancies in the calculated results. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, the present invention provides a method for calculating the thermal conductivity of quartz sandstone using crystal structure.

[0005] The main calculation steps of this invention are as follows:

[0006] S1. Clean the collected quartz sandstone sample, removing any loose soil or other substances from the surface. Place the clean quartz sandstone sample in a vacuum drying oven for vacuum drying at 110℃. The drying time needs to exceed 36 hours, until the sample weight no longer changes.

[0007] S2 uses Archimedes' method of buoyancy to measure the density of quartz sandstone, and uses nitrogen gas as the buoyancy medium to test the true density of the quartz sandstone sample: In the formula, ρ is the density of quartz sandstone, and w air For the mass of air, ρ Let w be the density of nitrogen gas. Nitrogen This represents the mass of nitrogen gas.

[0008] S3 used the volumetric flask method to test the apparent relative density of quartz sandstone and calculated its porosity: In the formula, φ represents the porosity of the quartz sandstone (%), and TRD represents the true relative density of the quartz sandstone (g / cm³). 3 ARD represents the apparent relative density of quartz sandstone, in g / cm³. 3 .

[0009] S4 uses XRD to obtain mineral content data and 2θ angle and peak intensity data in quartz sandstone.

[0010] S5 Since the mineral composition data of quartz sandstone obtained by XRD is in terms of weight percentage of mineral content, the weight percentage of mineral composition content is converted to volume percentage: In the formula, w i The percentage of weight obtained through XRD experiments is %; v i The calculated volume percentage is %; ρ i This represents the density of the mineral, in g / cm³. 3 .

[0011] S6 Considering the influence of quartz crystal structure on the thermal conductivity of quartz sandstone, and the difficulty in accurately calculating the specific value of thermal conductivity of quartz sandstone using traditional prediction models, this invention specifically uses quartz crystal structure parameters to correct the thermal conductivity value of quartz sandstone. First, XRD is used to obtain quartz crystal structure data in the sample. XRD experiments can obtain the 2θ angle of characteristic peaks of different crystal planes of quartz crystal. This invention uses the data of the most typical characteristic crystal planes 101 and 100 of quartz crystal for the following calculation.

[0012] Calculate the quartz unit cell data using the following formula: , , V e =a×b×c×sin(γ), In the formula, a, b, and c are the structural parameters of the mineral crystal, a = b ≠ c; h, k, and l are Miller indices, d is the interplanar spacing, θ is the diffraction angle, and λ is the interplanar spacing. x It is the X-ray wavelength (Cu & K) α , λ x = 0.15406 nm); γ = 120°; λ v V is the cell correction factor for quartz sandstone. e The volume of the quartz unit cell obtained from the experimental test is Å. 3 Vs is the standard quartz unit cell volume, in Å. 3 .

[0013] S7 uses the Scherrer formula to calculate the grain size of quartz, which is then used as the grain correction factor for calculating the thermal conductivity of quartz sandstone. , In the formula, λ D λ is the grain correction factor for quartz sandstone, K is the full width at half maximum (FWHM) parameter for different XRD diffractometers, determined by instrument performance parameters, typically 0.89, β is the full width at half maximum (FWHM) of the diffraction peak, in rad; λ x X-ray wavelength, nm.

[0014] S8. Quartz crystallinity is used as the macroscopic crystallinity correction coefficient for the thermal conductivity of quartz sandstone: , In the formula, F is the crystallinity coefficient of the XRD instrument, typically 1.1; a is the intensity difference between the diffraction peak at 2θ = 67.74° and the trough at 2θ = 67.85°; and b is the intensity of the peak at 2θ = 67.74°. λ QF This is the crystallinity correction factor for quartz sandstone.

[0015] S9. Based on the above results, the method for calculating the thermal conductivity of quartz sandstone is as follows: ;

[0016] In the formula, λ qz λ represents the thermal conductivity of quartz sandstone, in W / (m·K); q Thermal conductivity of different types of standard quartz, W / (m·K); n q λ represents the volume percentage of quartz minerals. v λ is the cell correction factor for quartz sandstone. QF λ is the crystallinity correction factor for quartz sandstone. D λ is the grain correction factor for quartz sandstone. i n represents the thermal conductivity of minerals other than quartz within the quartz sandstone. i denoted as the volume percentage of the mineral (%), φ as the porosity of the quartz sandstone (%), and λ as the porosity of the quartz sandstone. a ν is the thermal conductivity of air, W / (m·K).

[0017] Compared with the prior art, the beneficial effects of the present invention are:

[0018] 1. The thermal conductivity value of quartz sandstone is corrected by using standard quartz crystal structure data, which avoids the deviation in thermal conductivity calculation caused by the inability of traditional methods to respond in time to microscopic changes in quartz crystals.

[0019] 2. The thermal conductivity of quartz sandstone can be calculated and predicted using XRD test data, which effectively reduces the cost and workload of calculating the thermal conductivity of quartz sandstone.

[0020] 3. The thermal conductivity of quartz sandstone can be calculated using microscopic data of quartz sandstone, avoiding the limitation of using regular samples in traditional thermal conductivity testing methods. This greatly expands the value of cuttings used in oil and gas drilling and solves the problem that thermal conductivity cannot be measured because traditional methods cannot drill out complete samples. Detailed Implementation

[0021] The feasibility and applicability of this invention are analyzed below using actual data from quartz sandstone in a certain region of Southwest China as an example. For ease of understanding and calculation, all matrices in this invention will be presented in tabular form, with specific information annotated in the first row and first column of each table.

[0022] S1 shows the apparent density of the collected quartz sandstone samples (Table 1).

[0023] The true density of the quartz sandstone sample was obtained by experiment S2 (Table 1).

[0024] The apparent density of quartz sandstone was obtained and the porosity was calculated in experiment S3 (Table 1).

[0025] Table 1. Basic Data Table for Quartz Sandstone

[0026]

[0027] S4 Mineral content data (Table 1) and 2θ angle and peak intensity data (Table 2) of quartz sandstone were obtained using XRD.

[0028] Table 2. XRD diffraction information of quartz sandstone

[0029]

[0030] S5 converts the weight percentage of quartz sandstone to volume percentage, and the conversion results are as follows:

[0031] Table 3. Mineral volume content of quartz sandstone

[0032]

[0033] S6 Calculate the cell correction factor λ of quartz sandstone v ;

[0034] λ can be obtained by calculation. v =1.001;

[0035] S7 Calculate the grain correction factor λ for quartz sandstone. D ;

[0036] λ can be obtained by calculation. D =0.7424;

[0037] S8 Calculation of the crystallinity correction factor λ for quartz sandstone QF ;

[0038] λ can be obtained by calculation. QF =0.1001;

[0039] S9 Calculate the thermal conductivity of quartz sandstone;

[0040] The calculation yields λ = 2.55 W / (m·K);

[0041] The thermal conductivity of sample S10 was measured in an indoor laboratory and found to be 3.08 W / (m·K). The relative error is: R e =100*(3.08-2.55) / 3.68=17%.

[0042] The relative error is within an acceptable range, which proves the feasibility and accuracy of the present invention.

Claims

1. A method for calculating the thermal conductivity of quartz sandstone using crystal structure, characterized in that, Includes the following steps: S1. Clean the collected quartz sandstone sample, remove the surface material, and place the clean quartz sandstone sample in a vacuum drying oven for vacuum drying at a temperature of 110℃. The drying time should be no less than 36 hours, until the weight of the sample no longer changes. S2 uses Archimedes' method of buoyancy to measure the density of quartz sandstone, and uses nitrogen gas as the buoyancy medium to test the true density of the quartz sandstone sample: ； In the formula, ρ is the density of quartz sandstone, and w air Let ρ be the mass of air, ρ be the density of nitrogen, and w be the mass of air. Nitrogen The mass of nitrogen; S3 used the volumetric flask method to test the apparent relative density of the quartz sandstone and calculated its porosity: ； In the formula, φ represents the porosity of the quartz sandstone (%), and TRD represents the true absolute density of the quartz sandstone (g / cm³). 3 ARD represents the apparent relative density of quartz sandstone, in g / cm³. 3 ; S4. Mineral content data and 2θ angle and peak intensity data in quartz sandstone were obtained using XRD. S5 converts the weight percentage of mineral components to volume percentage: ； In the formula, w i The percentage of weight obtained through XRD experiments is %; v i The calculated volume percentage is % ρ i This represents the density of the mineral, in g / cm³. 3 ; S6 uses quartz crystal structure parameters to correct the thermal conductivity value of quartz sandstone; First, XRD was used to obtain the quartz crystal structure data in the sample. XRD experiments can obtain the 2θ angle of the characteristic peaks of different crystal planes of quartz crystal. The data of the most typical characteristic crystal planes 101 and 100 of quartz crystal were used for calculation. S7 uses the Scherrer formula to calculate the grain size of quartz, which is used as the grain correction factor for the calculation of thermal conductivity of quartz sandstone. S8. Quartz crystallinity is used as the macroscopic crystallinity correction coefficient for the thermal conductivity of quartz sandstone. S9. Based on the above results, calculate the thermal conductivity of quartz sandstone.

2. The method for calculating the thermal conductivity of quartz sandstone using crystal structure according to claim 1, characterized in that, In S6, the quartz unit cell data is calculated using the following formula: , , ,V e =a×b×c×sin(γ), ; In the formula, a, b, and c are the structural parameters of the mineral crystal, a = b ≠ c; h, k, and l are Miller indices, d is the interplanar spacing, θ is the diffraction angle, and λ is the interplanar spacing. x It is the X-ray wavelength (Cu & K) α , λ x = 0.15406 nm); γ = 120°; λ v V is the cell correction factor for quartz sandstone. e The volume of the quartz unit cell obtained from the experimental test, Å 3 Vs is the standard quartz unit cell volume, in Å. 3 .

3. The method for calculating the thermal conductivity of quartz sandstone using crystal structure according to claim 2, characterized in that, Grain correction factor for calculating the thermal conductivity of quartz sandstone in S7: ， ； In the formula, λ D λ is the grain correction factor for quartz sandstone, K is the full width at half maximum (FWHM) parameter for different XRD diffractometers, determined by the instrument performance parameters, β is the full width at half maximum (FWHM) of the diffraction peak, in rad; x X-ray wavelength, nm.

4. The method for calculating the thermal conductivity of quartz sandstone using crystal structure according to claim 3, characterized in that, In S8, the macroscopic crystallinity correction factor for the thermal conductivity of quartz sandstone is: ， ； In the formula, F is the crystallinity coefficient of the XRD instrument, typically 1.1; a is the intensity difference between the diffraction peak at 2θ = 67.74° and the trough at 2θ = 67.85°; b is the intensity of the peak at 2θ = 67.74°; λ QF This is the crystallinity correction factor for quartz sandstone.

5. The method for calculating the thermal conductivity of quartz sandstone using crystal structure according to claim 4, characterized in that, In S9, the thermal conductivity of quartz sandstone is calculated as follows: ； In the formula, λ qz λ represents the thermal conductivity of quartz sandstone, in W / (m·K); q Thermal conductivity of different types of standard quartz, W / (m·K); n q λ represents the volume percentage of quartz minerals. v λ is the cell correction factor for quartz sandstone. QF λ is the crystallinity correction factor for quartz sandstone. D λ is the grain correction factor for quartz sandstone. i n represents the thermal conductivity of minerals other than quartz within the quartz sandstone. i denoted as the volume percentage of the mineral (%), φ as the porosity of the quartz sandstone (%), and λ as the porosity of the quartz sandstone. a ν is the thermal conductivity of air, W / (m·K).

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