Method for predicting adsorption property of gas in shale through improved E-L-F model

Abstract

The invention discloses a method for predicting the adsorption property of gas in shale through an improved E-L-F model, and relates to the technical field of unconventional oil and gas development and carbon dioxide geological sequestration, and the method comprises the steps: providing an L-F improved adsorption model based on an L-F adsorption model in combination with a Langmuir + k isothermal adsorption model; based on the L-F improved adsorption model, an improved E-L-F adsorption model is provided in combination with an E-L adsorption model; and the precision of the improved E-L-F adsorption model is verified through experimental data fitting. According to the method, by fusing the Langmuir theory, the Freundlich theory and the Extended-Langmuir theory, an adsorbent heterogeneity parameter n, a high-pressure empirical parameter k and a parameter eta i representing the proportion of adsorption gas to adsorption sites are introduced, the surface characteristics and the high-pressure effect of an adsorption layer are effectively corrected, and the prediction precision of the adsorption amount of CH4 and CO2 in shale is remarkably improved. Experiments show that the average absolute relative deviation of the model in a single-component system and a mixed gas system is lower than 2.3%, and the model is suitable for optimal design of a CO2 enhanced shale gas exploitation technology and CO2 safety storage assessment.

Description

Technical Field

[0001] The invention relates to the technical field of unconventional oil and gas development and carbon dioxide geological storage, and in particular to a method for predicting gas adsorption properties in shale using an improved ELF model. Background Art

[0002] In recent years, the consumption of fossil fuels has caused a large amount of carbon dioxide emissions, leading to global warming. Carbon capture, utilization and storage (CCUS) is considered to be an effective technology to achieve CO2 emission reduction and mitigate the greenhouse effect. CO2 enhanced shale gas recovery technology (CO2-ESGR) is a very potential CCUS technology that can not only store a large amount of CO2, but also improve the recovery rate of shale gas. In this technology, the adsorption characteristics of CH4 and CO2 in shale directly affect the displacement effect and the safety of CO2 storage. Therefore, the study of CH4-CO2 adsorption characteristics in shale has important scientific value and research significance.

[0003] In the study of shale gas adsorption models, the most widely used is the traditional Langmuir model, but this model has the problem of insufficient prediction accuracy due to its single parameters and reliance on experimental data fitting, especially under high pressure conditions and mixed gas systems. In addition, existing research on the prediction model of the adsorption characteristics of the CH4-CO2 mixed system is relatively scarce, which is difficult to meet the application requirements under complex multivariable conditions. Further improvement is needed to propose a prediction model that can accurately predict the adsorption characteristics of the CH4-CO2 mixed gas system. Summary of the invention

[0004] In order to solve the above technical problems, the present invention discloses a method for predicting the gas adsorption properties in shale using an improved ELF model. The model combines the Langmuir+k model, the LF model and the EL model, and comprehensively considers the uneven surface of the adsorption layer and the high pressure conditions during the CH4-CO2 adsorption process of shale. While improving the prediction accuracy of the adsorption characteristics of single-component gases CH4 and CO2, the model realizes the accurate measurement of the adsorption amount of each component of CH4 and CO2 in the CH4-CO2 mixed system.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] A method for predicting gas adsorption properties in shale using an improved ELF model includes the following steps:

[0007] S1. Based on the LF adsorption model and combined with the Langmuir+k isotherm adsorption model, an improved LF adsorption model is proposed;

[0008] S2, based on the LF improved adsorption model and combined with the EL adsorption model, an improved ELF adsorption model is proposed;

[0009] S3. Verify the accuracy of the improved ELF adsorption model by fitting experimental data.

[0010] Optionally, in step S1, the LF improved adsorption model introduces the high-pressure empirical parameter k of the Langmuir+k isotherm adsorption model on the basis of the LF adsorption model, comprehensively considers the surface heterogeneity of the adsorbent and the high-pressure conditions, expands the application range of the LF adsorption model, improves the prediction accuracy, and solves the problem of poor prediction accuracy of the LF adsorption model under high-pressure conditions, wherein,

[0011] The LF adsorption model formula is: ;

[0012] The Langmuir+k isotherm adsorption model formula is: ;

[0013] The formula of LF improved adsorption model is: ;

[0014] Where N ab is the absolute amount of gas adsorption, mmol / g; K0 is the key parameter of the Langmuir model, which is the Langmuir pressure P L The reciprocal of K0=1 / P L , MPa -1 ; Q0 is the saturated adsorption capacity, mmol / g; P is the system pressure, MPa; k is the empirical parameter of the model fitting under high pressure conditions, dimensionless; n is a model parameter related to temperature and pore size distribution that represents the heterogeneity of the adsorbent, which is used to correct the adsorption position and adsorbed molecules.

[0015] Optionally, in step S2, the LF improved adsorption model established in step S1 can better predict the adsorption amount of single-component gases CH4 and CO2, but the prediction effect is poor for the CH4-CO2 mixed system; therefore, based on the LF improved adsorption model, combined with the EL adsorption model that can predict the adsorption amount of each component in the mixed gas, the improved ELF adsorption model is proposed by comprehensively considering the uneven surface of the adsorption layer and the high pressure conditions during the CH4-CO2 adsorption process of shale; this model can not only predict the adsorption amount of single components CH4 and CO2 and the CH4-CO2 mixed system in shale, but also predict the adsorption amount of each component CH4 and CO2 in the CH4-CO2 mixed system; compared with the LF improved adsorption model, the improved ELF adsorption model improves the prediction accuracy while expanding the application range of the model, and can effectively predict the adsorption properties of CH4-CO2 in shale. Among them,

[0016] The EL adsorption model formula is: ;

[0017] The improved ELF adsorption model formula is: ;

[0018] Where, the subscript i represents the gas component; N is the number of gas components, η i is a model parameter representing the proportion of adsorption sites occupied by adsorbed gas.

[0019] The invention has the beneficial effect that the invention discloses a method for predicting the gas adsorption properties in shale using an improved ELF model, which introduces the adsorbent heterogeneity parameter n, the high pressure empirical parameter k and the parameter η representing the proportion of adsorbed gas occupying adsorption sites by integrating Langmuir, Freundlich and Extended-Langmuir theories. i , effectively correcting the surface characteristics of the adsorption layer and the high-pressure effect, significantly improving the prediction accuracy of CH4 and CO2 adsorption in shale, and realizing the accurate measurement of the adsorption of each component of CH4 and CO2 in the CH4-CO2 mixed system. Experiments show that the average absolute relative deviation of the model in single-component and mixed gas systems is less than 2.3%, which is suitable for the optimization design of CO2 enhanced shale gas extraction technology and the evaluation of CO2 safe storage. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a method for predicting gas adsorption properties in shale using an improved ELF model of the present invention;

[0021] Figure 2A The adsorption fitting curves of LF model, EL model and improved ELF adsorption model for CH4 single component gas;

[0022] Figure 2B The adsorption fitting curves of LF model, EL model and improved ELF adsorption model for CO2 single component gas;

[0023] Figure 3A This is the relative error diagram between the LF model fitting results and the experimental values ​​of CH4 single-component gas;

[0024] Figure 3B This is the relative error diagram between the fitting results of the LF model for CO2 single-component gas and the experimental values;

[0025] Figure 3C This is the relative error diagram between the CH4 single-component gas EL model fitting results and the experimental values;

[0026] Figure 3DThis is the relative error diagram between the fitting results of the CO2 single-component gas EL model and the experimental value;

[0027] Figure 3E This is the relative error diagram between the ELF model fitting results of CH4 single-component gas and the experimental value;

[0028] Figure 3F This is the relative error diagram between the ELF model fitting results of CO2 single-component gas and the experimental value;

[0029] Figure 4A The adsorption fitting curves of LF model, EL model and improved ELF adsorption model for CH4-CO2 mixed gas with CO2 content of 80%;

[0030] Figure 4B The adsorption fitting curves of LF model, EL model and improved ELF adsorption model for CH4-CO2 mixed gas with CO2 content of 25%;

[0031] Figure 5A The fitting curves of the total CH4-CO2 adsorption, CH4 component adsorption and CO2 component adsorption in the CH4-CO2 mixed system with a CO2 content of 15% for the improved ELF adsorption model;

[0032] Figure 5B The fitting curves of the total CH4-CO2 adsorption, CH4 component adsorption and CO2 component adsorption in the CH4-CO2 mixed system with a CO2 content of 80% for the improved ELF adsorption model;

[0033] Fig. 6A This is the relative error diagram between the LF model fitting results of CH4-CO2 mixed gas and the experimental value;

[0034] Figure 6B This is the relative error diagram between the EL model fitting results of CH4-CO2 mixed gas and the experimental value;

[0035] Figure 6C This is the relative error diagram between the ELF model fitting results and the experimental values ​​of the CH4-CO2 mixed gas. DETAILED DESCRIPTION

[0036] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0037] A method for predicting gas adsorption properties in shale using an improved ELF model, such as Figure 1 As shown, the following steps are included:

[0038] S1. Based on the Langmuir and Freundlich adsorption theories, the LF adsorption model was combined with the Langmuir+k isotherm adsorption model to propose an improved LF adsorption model.

[0039] The LF adsorption model formula is: ;

[0040] The Langmuir+k isotherm adsorption model formula is: ;

[0041] The formula of LF improved adsorption model is: ;

[0042] Where N ab is the absolute amount of gas adsorption, mmol / g; K0 is the key parameter of the Langmuir model, which is the Langmuir pressure P L The reciprocal of K0=1 / P L , MPa -1 ; Q0 is the saturated adsorption capacity, mmol / g; P is the system pressure, MPa; k is the empirical parameter of the model fitting under high pressure conditions, dimensionless; n is a model parameter related to temperature and pore size distribution that represents the heterogeneity of the adsorbent, which is used to correct the adsorption position and adsorbed molecules.

[0043] S2. Based on the LF improved adsorption model, combined with the EL adsorption model that can predict the adsorption amount of each component in the mixed gas, the improved ELF adsorption model is proposed by comprehensively considering the uneven surface of the adsorption layer and the high pressure conditions during the CH4-CO2 adsorption process in shale; this model can not only predict the adsorption amount of CH4, CO2 single components and CH4-CO2 mixed system in shale, but also predict the adsorption amount of each component of CH4 and CO2 in the CH4-CO2 mixed system;

[0044] The EL adsorption model formula is: ;

[0045] The improved ELF adsorption model formula is: ;

[0046] Where, the subscript i represents the gas component; N is the number of gas components, η i is a model parameter representing the proportion of adsorption sites occupied by adsorbed gas.

[0047] S3. Verify the accuracy of the improved ELF adsorption model by fitting experimental data.

[0048] Example 1

[0049] Using the improved ELF adsorption model of the present invention, the adsorption results of single-component gases CH4 and CO2 on different shale samples were fitted at different temperatures and pressures to obtain the key parameters of the model fitting results. The specific steps are as follows:

[0050] S1. Using the improved ELF adsorption model proposed in the present invention, the absolute adsorption amount of CH4 and CO2 single-component gases on shale samples with a TOC content of 1.05% to 5.15% was fitted at a temperature of 303 to 353 K, and the key parameter K of the model was obtained by fitting. 0i , Q 0i , η i 、n i and k i , using the coefficient of determination R 2 To evaluate the fitting effect, R 2 The larger it is, the higher the accuracy of the model fitting.

[0051] Tables 1 and 2 show the fitting results and determination coefficients of key parameters of the improved ELF adsorption model for single-component gases CH4 and CO2, respectively.

[0052] Table 1

[0053]

[0054] As shown in Table 1, for CH4 single-component gas, the key parameter K of the improved ELF adsorption model fitting is0i 0.1043~0.4717, Q 0i is 0.0681~0.1968, η i is 0.7317~2.2816, k i -2.5018~-0.9316, n i The model fitting R 2 The average R 2 It is 0.9856. It can be seen that the fitting accuracy of the improved ELF adsorption model is higher.

[0055] Table 2

[0056]

[0057] As shown in Table 2, for CO2 single-component gas, the key parameter K of the improved ELF adsorption model fitting is 0i 0.1049~1.4107, Q 0i is 0.1041~0.3968, η i 0.7698~1.8566, k i -2.0519~-1.0017, n i The model fitting R 2 The average R 2 It is 0.9858, which shows that the fitting accuracy of the improved ELF adsorption model is higher.

[0058] S2. Based on step S1, the absolute adsorption amount of single-component gases CH4 and CO2 is fitted using the LF model and the EL model, and compared with the fitting results of the improved ELF adsorption model, the relative error between the model prediction value and the experimental value is calculated to verify the accuracy of the improved model prediction.

[0059] Figure 2A and Figure 2B The fitting curves of the LF model, EL model and improved ELF adsorption model for the CH4 and CO2 single-component gas adsorption experimental data under the conditions of TOC content of 3.64% and temperature of 303 K and 353 K are shown respectively. It can be seen from the figure that the improved ELF adsorption model has the highest fitting accuracy, R 2 At around 0.98, the fitting accuracy of the LF model and the EL model is low, and R 2Around 0.95; below low-order pressure (4 MPa), the fitting accuracy of the LF model, EL model and improved ELF adsorption model is not much different. After exceeding 4 MPa, the fitting curve of the improved ELF adsorption model is closer to the experimental data points, and the fitting curves of the LF model and the EL model deviate from the experimental values. Among them, the fitting curve of the LF model is lower than the experimental value, and the fitting curve of the EL model is higher than the experimental value.

[0060] FIG. 3A to FIG. 3F The relative error diagram of the fitting results and experimental values ​​of the LF model, EL model and improved ELF adsorption model for single-component gas of CH4 and CO2 is shown. As can be seen from the figure, for single-component gas of CH4, the relative deviations of the predicted values ​​of the LF model and EL model from the experimental values ​​are -5.5%~5.5%, and the average absolute relative deviations AARD are 2.76% and 2.64%, respectively; the relative deviations of the predicted values ​​of the improved ELF adsorption model from the experimental values ​​are -4.5%~4.5%, and the average absolute relative deviations are 2.24%, and the prediction accuracy is higher than that of the LF model and EL model. For single-component gas of CO2, the relative deviations of the predicted values ​​of the LF model and EL model from the experimental values ​​are -5.5%~5.5%, and the average absolute relative deviations are 2.78% and 2.69%, respectively; the relative deviations of the predicted values ​​of the improved ELF adsorption model from the experimental values ​​are -4.5%~4.5%, and the average absolute relative deviations are 2.26%, and the prediction accuracy is higher than that of the LF model and EL model. It can be seen that for single-component gases such as CH4 and CO2, the improved ELF adsorption model has higher prediction accuracy than the LF model and EL model.

[0061] Example 2

[0062] Using the improved ELF adsorption model proposed in the present invention, the adsorption results of CH4-CO2 mixed gas on different shale samples are fitted at different temperatures and pressures to obtain the key parameters of the model fitting results. The specific steps are as follows:

[0063] S1. Using the proposed improved ELF adsorption model, the absolute adsorption amount of CH4-CO2 mixed gas on shale samples with TOC content of 1.8% to 3.64% was fitted when the temperature was 278-353 K and the CO2 content was 8% to 80%. The key parameter K of the model was obtained by fitting. 0i , Q 0i , η i 、n i and k i , using the coefficient of determination R 2 To evaluate the fitting effect, R 2 The larger it is, the higher the accuracy of the model fitting.

[0064] Table 3 shows the key parameter fitting results and determination coefficients of the improved ELF adsorption model for CH4-CO2 mixed gas. As shown in Table 3, for CH4-CO2 mixed gas, the key parameter K 0i 0.1125~1.1205, Q 0i is 0.0757~0.3246, η i is 0.9578~1.4946, k i -2.5538~-0.9803, n i The model fitting R 2 The average R 2 It is 0.9859, which shows that the fitting accuracy of the improved ELF adsorption model is higher.

[0065] Table 3

[0066]

[0067] S2. Based on step S1, the absolute adsorption amount of CH4-CO2 mixed gas is fitted using the LF model and the EL model, and compared with the fitting results of the improved ELF adsorption model, the relative error between the model prediction value and the experimental value is calculated, and the accuracy of the improved model prediction is verified.

[0068] Figure 4A and Figure 4B The fitting curves of LF model, EL model and improved ELF adsorption model for CH4-CO2 mixed gas adsorption experimental data under the conditions of CO2 content of 80% and 25%, TOC content of 1.85% and 3.64%, and temperature of 303 K~363 K are shown in the figure. It can be seen from the figure that the improved ELF adsorption model has the highest fitting accuracy, R 2 At around 0.98, the fitting accuracy of the LF model and the EL model is low, and R 2 Around 0.95; below low-order pressure (3 MPa), the fitting accuracy of the LF model, EL model and improved ELF adsorption model is not much different. After exceeding 3 MPa, the fitting curve of the improved ELF adsorption model is closer to the experimental data points, the fitting curve of the LF model is lower than the experimental value, and the fitting curve of the EL model is higher than the experimental value, which is similar to the fitting results of single-component gases such as CH4 and CO2.

[0069] Figure 5A and Figure 5BThe following are the fitting curves of the total CH4-CO2 adsorption, CH4 component adsorption and CO2 component adsorption of the improved ELF adsorption model in the CH4-CO2 mixed gas adsorption experiment under the conditions of 15% and 80% CO2 content, 3.18% TOC content and 313 K. It can be seen from the figure that the fitting curve of the CH4-CO2 mixed gas adsorption by the improved ELF adsorption model is basically consistent with the experimental data points, and the average R 2 It is 0.9847. It can be seen that the improved ELF adsorption model has a good prediction ability for the total CH4-CO2 adsorption, CH4 component adsorption and CO2 component adsorption in the CH4-CO2 mixed system under the conditions of CO2 content of 15% and 85%, TOC content of 3.18% and temperature of 313 K.

[0070] FIG. 6A to FIG. 6C The figure shows the relative error between the fitting results of the LF model, EL model and improved ELF adsorption model for CH4-CO2 mixed gas and the experimental values. As can be seen from the figure, for CH4-CO2 mixed gas, the relative deviation between the predicted values ​​of the LF model and the EL model and the experimental values ​​is -5.5%~5.5%, and the average absolute relative deviation AARD is 2.81% and 2.73%, respectively; the relative deviation between the predicted values ​​of the improved ELF adsorption model and the experimental values ​​is -4.5%~4.5%, and the average absolute relative deviation is 2.29%, and the prediction accuracy is higher than that of the LF model and the EL model. It can be seen that for CH4-CO2 mixed gas, the improved ELF adsorption model has a higher prediction accuracy than the LF model and the EL model.

[0071] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for predicting gas adsorption properties in shale using an improved ELF model, characterized in that: The steps include: S1. Based on the LF adsorption model and combined with the Langmuir+k isotherm adsorption model, an improved LF adsorption model is proposed; S2. Based on the LF improved adsorption model, combined with the EL adsorption model for predicting the adsorption amount of each component in the mixed gas, the improved ELF adsorption model is proposed by comprehensively considering the uneven surface of the adsorption layer and the high pressure conditions during the CH4-CO2 adsorption process of shale; S3. Verify the accuracy of the improved ELF adsorption model by fitting experimental data.

2. The method for predicting gas adsorption properties in shale using an improved ELF model according to claim 1, characterized in that: In step S1, The LF adsorption model formula is: ; The Langmuir+k isotherm adsorption model formula is: ; The formula of LF improved adsorption model is: ; Where N ab is the absolute amount of gas adsorption, mmol / g; K0 is the key parameter of the Langmuir model, which is the Langmuir pressure P L The reciprocal of K0=1 / P L , MPa -1 ; Q0 is the saturated adsorption capacity, mmol / g; P is the system pressure, MPa; k is the empirical parameter of the model fitting under high pressure conditions, dimensionless; n is a model parameter related to temperature and pore size distribution that represents the heterogeneity of the adsorbent, which is used to correct the adsorption position and adsorbed molecules.

3. The method for predicting gas adsorption properties in shale using an improved ELF model according to claim 1, characterized in that: In step S2, The EL adsorption model formula is: ; The improved ELF adsorption model formula is: ; Where, the subscript i represents the gas component; N is the number of gas components, η i is a model parameter representing the proportion of adsorption sites occupied by adsorbed gas.

Images