Method and device for calculating thermophysical property of gasification working medium

Abstract

The invention discloses a method and a device for calculating the thermophysical property of a gasification working medium based on a Wirie equation and a residual entropy scaling method, which can be applied to the technical field of power engineering and engineering thermophysics. The method comprises the following steps: calculating a comparison second Wirie coefficient and a comparison third Wirie coefficient of each component based on a state parameter of a gasification working medium and a physical property parameter of each component; calculating a second Wirie coefficient and a third Wirie coefficient of the gasification working medium based on the above parameters by using a mixing rule; calculating the density of the gasification working medium by adopting a Wirie equation according to the state parameters, the second Wirie coefficient and the third Wirie coefficient; according to the state parameter, the density, the second Wirie coefficient and the third Wirie coefficient, the thermodynamic property of the gasification working medium is calculated; on the basis of the physical property parameters and the state parameters of all the components, the rarefied gas transportation property of the gasification working medium is calculated; and calculating the transportation property of the gasification working medium by using a residual entropy scaling method according to the residual entropy and the transportation property of the rarefied gas.

Description

Technical Field

[0001] This application relates to the fields of power engineering and engineering thermophysics, specifically to a method and apparatus for calculating the thermophysical properties of gaseous substances based on the virial equation and the residual entropy scaling method. Background Technology

[0002] Gasification technology efficiently converts solid or liquid fuels into syngas, playing a vital role in modern energy and chemical industries. Syngas (whose main active components include hydrogen, carbon monoxide, and methane) and its combustion products (mainly water vapor, carbon dioxide, nitrogen, and oxygen) produced from coal, biomass, and other raw materials through gasification technology are widely used in high-efficiency energy conversion systems such as integrated gasification combined cycle (IGCC), constituting a key working fluid for these systems. Due to the complex and diverse composition of gasified fluids, their thermophysical parameters vary significantly over a wide range of temperature and pressure. Therefore, accurately calculating the thermophysical properties (including density, specific heat, velocity of sound, viscosity, and thermal conductivity) of gasified fluids over a broad temperature and pressure range has become an important requirement.

[0003] Currently, calculations of the thermophysical properties of gasification mixtures typically employ experimental data interpolation or empirical models fitted from experimental data. However, acquiring experimental data is not only time-consuming and expensive, but also extremely difficult under high-temperature conditions. Existing experimental data is scarce, and in some cases, experimental data is completely lacking, severely limiting the computational capabilities of the models. Furthermore, because empirical models often lack a solid theoretical foundation, the reliability of the calculation results cannot be effectively guaranteed when dealing with mixed working fluids or operating conditions beyond the experimental range, greatly limiting the accuracy and efficiency of gasification system design and operational optimization. Summary of the Invention

[0004] To address at least some of the aforementioned technical problems, embodiments of this application provide a method and apparatus for calculating the thermophysical properties of gaseous chemicals based on the virial equation and the residual entropy scaling method.

[0005] This application provides a method for calculating the thermophysical properties of gaseous substances based on the virial equation and the residual entropy scaling method, including:

[0006] Based on the state parameters of the gasified substance and the physical properties of each component, the comparative second virial coefficient and comparative third virial coefficient of each component are calculated.

[0007] The second and third virial coefficients of the gasified substance are calculated using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second and third virial coefficients of each component.

[0008] The density of the gasified substance is calculated using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance.

[0009] The thermodynamic properties of the gasified substance are calculated based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include the residual entropy.

[0010] Based on the physical properties and state parameters of each component in the gasified substance, the rarefied gas transport properties of the gasified substance are calculated.

[0011] The transport properties of the gasified substance are calculated using the residual entropy scaling method, based on the residual entropy and the transport properties of the rarefied gas.

[0012] In some embodiments, for components in the gasified substance that are simple spherical fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0013]

[0014] In the formula,

[0015] This indicates the comparison of the second virial coefficient;

[0016] This indicates the comparison of the third dimensional coefficient;

[0017] This indicates that the simple spherical term in the second virial coefficient varies with the comparison temperature. A function relating change;

[0018] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0019] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0020] In some embodiments, for components in the gasified substance that are non-polar fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0021]

[0022] In the formula,

[0023] This indicates the comparison of the second virial coefficient;

[0024] This indicates the comparison of the third dimensional coefficient;

[0025] , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change;

[0026] This represents the eccentricity factor of the component;

[0027] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0028] This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change;

[0029] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0030] In some embodiments, for components in the gasified substance that are polar fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0031]

[0032] In the formula,

[0033] This indicates the comparison of the second virial coefficient;

[0034] This indicates the comparison of the third dimensional coefficient;

[0035] , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change;

[0036] This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment A function relating change;

[0037] This represents the eccentricity factor of the component;

[0038] This represents the contrast dipole moment of the component;

[0039] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0040] This indicates that the polarity term in the third virial coefficient of a polar fluid varies with the corresponding temperature. Eccentricity factor Contrast dipole moment A function relating change;

[0041] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0042] In some embodiments, for components in the gasified substance that are quantum fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formula:

[0043]

[0044] In the formula,

[0045] This indicates the comparison of the second virial coefficient;

[0046] This indicates the comparison of the third dimensional coefficient;

[0047] , This indicates that the simple spherical and quantum terms in the third virial coefficients vary with the comparison temperature. A function relating change;

[0048] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0049] This indicates the contrastive de Broglie wavelength of the component;

[0050] , These respectively represent the simple spherical term and the quantum term in the second virial coefficient as a function of the comparison temperature. A function relating change.

[0051] In some embodiments, for carbon dioxide in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of carbon dioxide are calculated according to the following formulas:

[0052]

[0053] In the formula,

[0054] The second virial coefficient representing the contrast of carbon dioxide;

[0055] The third virial coefficient representing the contrast of carbon dioxide;

[0056] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0057] This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change;

[0058] , Temperature represents the state parameters of a gaseous substance. Indicates the critical temperature of carbon dioxide;

[0059] The eccentricity factor represents carbon dioxide.

[0060] In some embodiments, for water in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of water are calculated according to the following formulas:

[0061]

[0062] In the formula,

[0063] The second virial coefficient representing the contrast of water;

[0064] The third virial coefficient representing the contrast of water;

[0065] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0066] , Temperature represents the state parameters of a gaseous substance. Indicates the critical temperature of water;

[0067] The eccentricity factor representing water;

[0068] This represents the contrast dipole moment of water.

[0069] In some embodiments, the calculation of the second and third virial coefficients of the gasified substance using mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second and third virial coefficients of each component includes:

[0070] Based on the critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength, and interaction coefficient of each component in the gasified propellant, the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed propellant composed of each pair of components are calculated.

[0071] Based on the temperature of the gasified substance and the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working substance composed of each of the two components, calculate the cross second virial coefficient of the mixed working substance composed of each of the two components.

[0072] The second virial coefficient of the gasified substance is calculated based on the cross-second virial coefficient of the mixed working substance composed of each of the two components in the gasified substance and the mole fraction of each component in the gasified substance.

[0073] Based on the comparative third virial coefficient of each of the three components in the gasified working fluid, the cross third virial coefficient of the mixed working fluid composed of the three components is calculated.

[0074] The third dimensional coefficient of the gasified substance is calculated based on the cross-third dimensional coefficient of the mixed working substance composed of three components in each gasified substance and the mole fraction of each component in the gasified substance.

[0075] In some embodiments, the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid composed of each of the two components in the gasification fluid are calculated based on the following formulas:

[0076]

[0077] In the formula,

[0078] , , , , Each is composed of pure working fluid components , The mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid.

[0079] , , , , The components are pure working fluids. Critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength;

[0080] , , , , The components are pure working fluids. Critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength;

[0081] pure working fluid component With pure working fluid components The interaction coefficient when the working fluid is mixed.

[0082] In some embodiments, the cross-second virial coefficient of the mixed working fluid composed of each of the two said components is calculated based on the following formula:

[0083]

[0084] In the formula,

[0085] pure working fluid component , The comparative second virial coefficient of the mixed working fluid;

[0086] Indicates a composition of pure working fluid elements , The cross-second virial coefficient of the mixed working fluid;

[0087] Indicates a composition of pure working fluid elements , The critical pressure of the mixture of working fluids;

[0088] Indicates a composition of pure working fluid elements , The critical mixing temperature of the mixed working fluid;

[0089] Represents the universal gas constant;

[0090] , , These respectively represent the simple spherical term, nonpolar term, and quantum term in the second virial coefficients as a function of the comparison temperature. A function relating change;

[0091] This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment A function relating change;

[0092] Indicates a composition of pure working fluid elements , The relative temperatures of the mixed working fluids. , Temperature represents the state parameters of a gaseous substance;

[0093] Indicates a composition of pure working fluid elements , The mixing eccentricity factor of the mixed working fluid;

[0094] Indicates a composition of pure working fluid elements , The mixed contrast dipole moment of the mixed working fluid;

[0095] Indicates a composition of pure working fluid elements , The mixing of the working fluids is compared with the de Broglie wavelength.

[0096] In some embodiments, the second virial coefficient of the gasified substance is calculated based on the following formula:

[0097]

[0098] In the formula,

[0099] This represents the second virial coefficient of the gasified substance;

[0100] , They represent the pure working fluid components in the mixed working fluid. , Their respective mole fractions;

[0101] Indicates a composition of pure working fluid elements , The cross-second virial coefficient of the mixed working fluid;

[0102] This indicates the number of pure working fluid components in the gasified chemical substance.

[0103] In some embodiments, the third-dimensional coefficient of the gasified substance is calculated based on the following formula:

[0104]

[0105] In the formula,

[0106] Indicates a composition of pure working fluid elements , , The cross-third virial coefficient of the mixed working fluid;

[0107] , , They represent the components of the pure working fluid, respectively. , , The coefficients in the third dimension;

[0108] This represents the third-dimensional coefficient of the gasified substance;

[0109] , , They represent the pure working fluid components in the mixed working fluid. , , Their respective mole fractions;

[0110] This indicates the number of pure working fluid components in the gasified chemical substance.

[0111] In some embodiments, the density of the gasified substance is calculated iteratively using the following formula:

[0112]

[0113] In the formula,

[0114] This indicates the density of the gasified substance;

[0115] Temperature represents the state parameters of a gaseous substance;

[0116] This represents the pressure in the state parameters of a gaseous substance.

[0117] Represents the universal gas constant;

[0118] This represents the second virial coefficient of the gasified substance;

[0119] The third-dimensional coefficient of the gasified substance is represented.

[0120] In some embodiments, the thermodynamic properties include residual internal energy, which is calculated according to the following formula:

[0121]

[0122] In the formula,

[0123] This represents the remaining internal energy of the gasified substance;

[0124] Represents the universal gas constant;

[0125] This refers to the temperature among the state parameters of the gasified substance;

[0126] This represents the second virial coefficient of the gasified substance;

[0127] This represents the third-dimensional coefficient of the gasified substance;

[0128] This indicates the density of the gasified chemical substance.

[0129] In some embodiments, the thermodynamic property includes internal energy, which is calculated according to the following formula:

[0130]

[0131]

[0132] In the formula,

[0133] This represents the internal energy of the gasified substance;

[0134] This represents the remaining internal energy of the gasified substance;

[0135] This represents the ideal internal energy of the gasified substance;

[0136] This refers to the temperature among the state parameters of the gasified substance;

[0137] This indicates the density of the gasified substance;

[0138] This represents the specific heat capacity at constant volume of an ideal gas in a gaseous chemical process.

[0139] This represents the specific heat capacity at constant pressure of an ideal gas.

[0140] Represents the universal gas constant;

[0141] , express The number of different types of related items;

[0142] , , , express The parameters of the related items.

[0143] In some embodiments, the thermodynamic property includes residual enthalpy, which is calculated according to the following formula:

[0144]

[0145] In the formula,

[0146] This indicates the residual enthalpy of the gasified substance;

[0147] Represents the universal gas constant;

[0148] This refers to the temperature among the state parameters of the gasified substance;

[0149] This represents the second virial coefficient of the gasified substance;

[0150] This represents the third-dimensional coefficient of the gasified substance;

[0151] This indicates the density of the gasified chemical substance.

[0152] In some embodiments, the thermodynamic property includes enthalpy, which is calculated according to the following formula:

[0153]

[0154]

[0155] In the formula,

[0156] This represents the enthalpy of the gasified substance;

[0157] This indicates the residual enthalpy of the gasified substance;

[0158] This represents the ideal enthalpy of the gasified substance;

[0159] This refers to the temperature among the state parameters of the gasified substance;

[0160] This indicates the density of the gasified substance;

[0161] This represents the ideal gas specific heat capacity at constant pressure for gasification.

[0162] In some embodiments, the thermodynamic property includes residual entropy, which is calculated according to the following formula:

[0163]

[0164] In the formula,

[0165] This represents the residual entropy of the gasified substance;

[0166] Represents the universal gas constant;

[0167] This refers to the temperature among the state parameters of the gasified substance;

[0168] This represents the second virial coefficient of the gasified substance;

[0169] This represents the third-dimensional coefficient of the gasified substance;

[0170] This indicates the density of the gasified chemical substance.

[0171] In some embodiments, the thermodynamic property includes entropy, which is calculated according to the following formula:

[0172]

[0173]

[0174] In the formula,

[0175] This represents the entropy of the gasified substance;

[0176] This represents the residual entropy of the gasified substance;

[0177] This represents the ideal entropy of the gasified substance;

[0178] Indicates reference state , The ideal entropy of the gasified substance is taken as ;

[0179] This represents the density of an ideal gaseous chemical substance under reference conditions. ;

[0180] Indicates the temperature under reference conditions;

[0181] Indicates the pressure under reference conditions;

[0182] This represents the specific heat capacity at constant pressure of an ideal gas in a gaseous chemical process.

[0183] This refers to the temperature among the state parameters of the gasified substance;

[0184] This indicates the density of the gasified substance;

[0185] This represents the universal gas constant.

[0186] In some embodiments, the thermodynamic properties include residual specific heat at constant volume, which is calculated according to the following formula:

[0187]

[0188] In the formula,

[0189] This represents the residual specific heat at constant volume of the gasified substance;

[0190] Represents the universal gas constant;

[0191] This refers to the temperature among the state parameters of the gasified substance;

[0192] This represents the second virial coefficient of the gasified substance;

[0193] This represents the third-dimensional coefficient of the gasified substance;

[0194] This indicates the density of the gasified chemical substance.

[0195] In some embodiments, the thermodynamic property includes specific heat at constant volume, which is calculated according to the following formula:

[0196]

[0197]

[0198] In the formula,

[0199] This represents the specific heat at constant volume of the gasified substance;

[0200] This represents the residual specific heat at constant volume of the gasified substance;

[0201] This represents the ideal isochoric specific heat of the gasified substance;

[0202] Represents the universal gas constant;

[0203] This represents the ideal gas specific heat capacity at constant pressure for gasification.

[0204] In some embodiments, the thermodynamic property includes residual isobaric specific heat, which is calculated according to the following formula:

[0205]

[0206]

[0207]

[0208] In the formula,

[0209] This represents the residual specific heat at constant pressure of the gasified substance;

[0210] This represents the residual specific heat at constant volume of the gasified substance;

[0211] Represents the universal gas constant;

[0212] This refers to the temperature among the state parameters of the gasified substance;

[0213] This indicates the pressure in the state parameters of the gasified substance;

[0214] This represents the second virial coefficient of the gasified substance;

[0215] This represents the third-dimensional coefficient of the gasified substance;

[0216] This indicates the density of the gasified chemical substance.

[0217] In some embodiments, the thermodynamic property includes isobaric specific heat, which is calculated according to the following formula:

[0218]

[0219] In the formula,

[0220] This indicates the specific heat at constant pressure of the gasified substance;

[0221] This represents the residual specific heat at constant pressure of the gasified substance;

[0222] This represents the ideal gas specific heat capacity at constant pressure for gasification.

[0223] In some embodiments, the thermodynamic property includes the speed of sound, which is calculated according to the following formula:

[0224]

[0225] In the formula,

[0226] The velocity of sound of the gasified substance is indicated.

[0227] Represents the universal gas constant;

[0228] This refers to the temperature among the state parameters of the gasified substance;

[0229] This indicates the ideal specific heat ratio of the gasified substance;

[0230] This indicates the relative molecular mass of the gasified chemical substance;

[0231] This represents the second virial coefficient of the speed of sound;

[0232] This represents the third-dimensional coefficient of the speed of sound;

[0233] This indicates the density of the gasified substance;

[0234] This represents the specific heat capacity at constant pressure of an ideal gas in a gaseous chemical process.

[0235] This represents the specific heat capacity at constant volume of an ideal gas in a gaseous chemical process.

[0236] This represents the second virial coefficient of the gasified substance;

[0237] The third-dimensional coefficient of the gasified substance is represented.

[0238] In some embodiments, the rarefied gas transport properties of the gasified substance are calculated according to the following formula:

[0239]

[0240]

[0241]

[0242] In the formula,

[0243] , These represent the rarefied gas transport properties of pure working fluid components i and j at temperature T, including viscosity η or thermal conductivity λ.

[0244] T represents the temperature in the state parameters of the gasified substance;

[0245] These are parameters representing the transport properties of rarefied gases that are specific to fluids.

[0246] This indicates the rarefied gas transport properties of a mixed gaseous chemical substance;

[0247] , These represent the mole fractions of pure working fluid components i and j in the mixed working fluid, respectively.

[0248] n represents the number of pure working substances in the gasification process;

[0249] The factor representing the influence of the mixture of component i and component j on transport properties;

[0250] , These represent the relative molecular masses of components i and j, respectively.

[0251] In some embodiments, the actual transport properties of the gasified substance are calculated according to the following formula:

[0252]

[0253]

[0254]

[0255] In the formula,

[0256] X represents the actual transport properties of the gasified substance;

[0257] This indicates the rarefied gas transport properties of a mixed gaseous chemical substance;

[0258] It is the dimensionless residual entropy;

[0259] These are fluid-specific residual transport property parameters. Represents the i-th type of element parameter;

[0260] Represents the mole fraction of the i-th component;

[0261] This represents the residual entropy of the gasified substance;

[0262] This refers to the temperature among the state parameters of the gasified substance;

[0263] This indicates the density of the gasified substance;

[0264] R represents the universal gas constant.

[0265] This application also provides a gasification thermophysical property calculation device based on the virial equation and the residual entropy scaling method, including:

[0266] The first calculation module is used to calculate the comparative second virial coefficient and the comparative third virial coefficient of each component based on the state parameters of the gasified substance and the physical property parameters of each component.

[0267] The second calculation module is used to calculate the second virial coefficient and the third virial coefficient of the gasified substance using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second virial coefficient and the comparative third virial coefficient of each component.

[0268] The third calculation module is used to calculate the density of the gasified substance using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance.

[0269] The fourth calculation module is used to calculate the thermodynamic properties of the gasified substance based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include residual entropy;

[0270] The fifth calculation module is used to calculate the rarefied gas transport properties of the gasified substance based on the physical properties and state parameters of each component in the gasified substance.

[0271] The sixth calculation module is used to calculate the transport properties of the gasified substance using the residual entropy scaling method, based on the residual entropy and the transport properties of the rarefied gas.

[0272] This application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the methods described in any of the above embodiments.

[0273] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described in any of the above embodiments.

[0274] This application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the methods described in any of the above embodiments.

[0275] The method and apparatus for calculating the thermal properties of gaseous substances based on the virial equation and the residual entropy scaling method provided in this application combine the virial equation and the residual entropy scaling method to achieve unified closed-loop calculation of density, thermodynamic properties, and transport properties. It has high engineering adaptability and can be used for calculating the thermal properties of gaseous substances with complex components. It can significantly improve the accuracy and reliability of the calculation of the thermal properties of gaseous substances, especially under conditions where experimental data is scarce, such as high temperature and high pressure, it has strong computational extrapolation capabilities. Attached Figure Description

[0276] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0277] Figure 1 This is a flowchart illustrating a gasification thermophysical property calculation method based on the virial equation and the residual entropy scaling method provided in an embodiment of this application.

[0278] Figure 2 The graph shows the calculated effective density and pressure as a function of temperature when the deviation from the multi-parameter equation of state for CO2 is 1%.

[0279] Figure 3The violin deviation plot was used to verify the comparison between the thermophysical properties of the pure substance calculated by this method and the experimental data.

[0280] Figure 4 The violin deviation plot was used to verify the thermophysical properties of the mixture calculated by this method with experimental data.

[0281] Figure 5 This is a schematic flowchart of a gasification thermophysical property calculation device based on the virial equation and the residual entropy scaling method provided in an embodiment of this application.

[0282] Figure 6 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0283] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the embodiments of this application will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and their descriptions are used to explain this application, but are not intended to limit this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily arranged.

[0284] The terms “first,” “second,” etc., used in this document are not intended to specifically refer to order or sequence, nor are they used to limit this application; they are merely used to distinguish elements or operations described using the same technical terms.

[0285] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.

[0286] The term "and / or" as used in this document includes any or all of the items mentioned.

[0287] To address the problems of existing technologies, such as strong reliance on experimental data, limited predictive applicability, and particular difficulty in accurately predicting the thermophysical properties of gaseous substances in high-temperature regions, this application proposes a method and apparatus for calculating the thermophysical properties of gaseous substances based on the virial equation and the residual entropy scaling method. This method is applicable not only to pure component gaseous substances but also to the efficient and accurate calculation of the thermophysical properties of complex mixed gaseous substances. Furthermore, it effectively compensates for the inadequacy of experimental data, especially in high-temperature and high-pressure regions where current experimental methods are not yet feasible, accurately calculating the thermophysical properties of gaseous substances. This provides more reliable thermophysical data support for the design, simulation, and optimization of systems using gaseous substances for work.

[0288] Figure 1 This is a schematic flowchart illustrating a method for calculating the thermophysical properties of gaseous substances based on the virial equation and the residual entropy scaling method, as provided in an embodiment of this application. Figure 1As shown in the embodiments of this application, a method for calculating the thermophysical properties of gasification materials based on the virial equation and the residual entropy scaling method is provided, including:

[0289] S1. Based on the state parameters of the gasified substance and the physical property parameters of each component, calculate the comparative second virial coefficient and comparative third virial coefficient of each component.

[0290] In step S1, the method proposed in this application is not only applicable to pure component gaseous substances, but also capable of efficiently and accurately calculating the thermal properties of complex mixed gaseous substances, including: hydrogen (H2), methane (CH4), carbon monoxide (CO), oxygen (O2), nitrogen (N2), water (H2O), carbon dioxide (CO2), etc. The state parameters of the gaseous substance may include temperature T and pressure p, and the physical property parameters of each component may include the critical temperature T. c Critical pressure p c and critical density ρ c eccentricity factor ω, contrast dipole moment μ is the dipole moment and mole fraction x i wait.

[0291] Based on the physical properties of each component and the state parameters of the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated.

[0292] S2. Using the mixing rule, calculate the second virial coefficient and the third virial coefficient of the gasified substance based on the state parameters, the physical property parameters of each component, and the comparative second virial coefficient and the comparative third virial coefficient of each component.

[0293] S3. Calculate the density of the gasified substance using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance.

[0294] S4. Calculate the thermodynamic properties of the gasified substance based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include the residual entropy;

[0295] In step S4, the thermodynamic properties may further include enthalpy h, entropy s, internal energy u, and specific heat at isobaric pressure c. p Specific heat at constant volume c v And the speed of sound w; where, apart from the speed of sound w, the other thermodynamic properties can be expressed as the sum of ideal gas properties (superscript 0 represents the ideal state) and residual properties (superscript r represents the residual state). The residual term represents the deviation of the actual thermodynamic properties from the ideal state, and is expressed as an expression related to temperature, density, and virial coefficient. The residual properties are determined by the virial equation, and the ideal gas properties are calculated through the ideal isobaric specific heat correlation.

[0296] S5. Based on the physical properties and state parameters of each component in the gasified substance, calculate the rarefied gas transport properties of the gasified substance.

[0297] S6. Using the residual entropy scaling method, calculate the transport properties of the gasified substance based on the residual entropy and the transport properties of the rarefied gas.

[0298] The gaseous material thermophysical property calculation method based on the virial equation and the residual entropy scaling method provided in this application combines the virial equation and the residual entropy scaling method to achieve unified closed-loop calculation of density, thermodynamic properties, and transport properties. It has high engineering adaptability and can be used for the thermophysical property calculation of gaseous materials with complex components. It can significantly improve the accuracy and reliability of the thermophysical property calculation of gaseous materials, especially under conditions where experimental data is scarce, such as high temperature and high pressure, it has strong computational extrapolation ability.

[0299] In some embodiments, in step S1 above, the fluid type of each component is first determined, and the classification method is as follows:

[0300] Simple spherical fluid: methane

[0301] Non-polar fluids: nitrogen, oxygen, carbon dioxide

[0302] Quantum fluid: hydrogen

[0303] Polar fluid: carbon monoxide

[0304] Associating fluid: water

[0305] Specific correlations: carbon dioxide, water.

[0306] After determining the fluid type for each component, the comparative second virial coefficient and comparative third virial coefficient for that component are calculated according to the fluid type of each component.

[0307] In some embodiments, for components of the gasified substance that are simple spherical fluids (e.g., methane), the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0308]

[0309]

[0310]

[0311]

[0312] In the formula,

[0313] This indicates the comparison of the second virial coefficient;

[0314] This indicates the comparison of the third dimensional coefficient;

[0315] This indicates that the simple spherical term in the second virial coefficient varies with the comparison temperature. A function relating change;

[0316] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0317] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0318] In some embodiments, for components of the gasified substance that are nonpolar fluids (e.g., nitrogen / oxygen), the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0319]

[0320]

[0321]

[0322]

[0323] In the formula,

[0324] This indicates the comparison of the second virial coefficient;

[0325] This indicates the comparison of the third dimensional coefficient;

[0326] , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change;

[0327] This represents the eccentricity factor of the component;

[0328] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change;

[0329] This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change;

[0330] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0331] In some embodiments, for components in the gasified substance that are polar fluids (such as carbon monoxide), the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0332]

[0333]

[0334]

[0335]

[0336] In the formula,

[0337] This indicates the comparison of the second virial coefficient;

[0338] This indicates the comparison of the third dimensional coefficient;

[0339] , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change; , The calculation formula is given in the foregoing embodiments;

[0340] This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment A function relating change;

[0341] This represents the eccentricity factor of the component;

[0342] This represents the contrast dipole moment of the component;

[0343] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; The calculation formula is given in the foregoing embodiments;

[0344] This indicates that the polarity term in the third virial coefficient of a polar fluid varies with the corresponding temperature. Eccentricity factor Contrast dipole moment A function relating change;

[0345] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0346] In some embodiments, for components of the gasified substance that are quantum fluids (such as hydrogen), the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas:

[0347]

[0348]

[0349]

[0350]

[0351] In the formula,

[0352] This indicates the comparison of the second virial coefficient;

[0353] This indicates the comparison of the third dimensional coefficient;

[0354] , This indicates that the simple spherical and quantum terms in the third virial coefficients vary with the comparison temperature. A function relating change; The calculation formula is given in the foregoing embodiments;

[0355] , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

[0356] This indicates the contrastive de Broglie wavelength of the component. (where h is Planck's constant and m is the molecular mass) and (These are molecular potential energy parameters).

[0357] , These respectively represent the simple spherical term and the quantum term in the second virial coefficient as a function of the comparison temperature. A function relating change; The calculation formula is described in the aforementioned embodiments.

[0358] In some embodiments, for carbon dioxide in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of carbon dioxide are calculated according to the following formulas:

[0359]

[0360]

[0361] In the formula,

[0362] The second virial coefficient representing the contrast of carbon dioxide;

[0363] The third virial coefficient representing the contrast of carbon dioxide;

[0364] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; The calculation formula is given in the foregoing embodiments;

[0365] This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change; The calculation formula is given in the foregoing embodiments;

[0366] , Temperature represents the state parameters of a gaseous substance. Indicates the critical temperature of carbon dioxide;

[0367] The eccentricity factor represents carbon dioxide.

[0368] In some embodiments, for water in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of water are calculated according to the following formulas:

[0369]

[0370]

[0371] In the formula,

[0372] The second virial coefficient representing the contrast of water;

[0373] The third virial coefficient representing the contrast of water;

[0374] This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; The calculation formula is given in the foregoing embodiments;

[0375] T r =T / T c T represents the temperature in the gasification state parameters. c Indicates the critical temperature of water;

[0376] ω represents the eccentricity factor of water;

[0377] This represents the contrast dipole moment of water.

[0378] In some embodiments, step S2 above may include:

[0379] Based on the critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength, and interaction coefficient of each component in the gasified propellant, the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed propellant composed of each pair of components are calculated.

[0380] Based on the temperature of the gasified substance and the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working substance composed of each of the two components, calculate the cross second virial coefficient of the mixed working substance composed of each of the two components.

[0381] The second virial coefficient of the gasified substance is calculated based on the cross-second virial coefficient of the mixed working substance composed of each of the two components in the gasified substance and the mole fraction of each component in the gasified substance.

[0382] Based on the comparative third virial coefficient of each of the three components in the gasified working fluid, the cross third virial coefficient of the mixed working fluid composed of the three components is calculated.

[0383] The third dimensional coefficient of the gasified substance is calculated based on the cross-third dimensional coefficient of the mixed working substance composed of three components in each gasified substance and the mole fraction of each component in the gasified substance.

[0384] It should be noted that a pure substance can be regarded as a mixture in which the mole fraction of one component is 1 and the mole fraction of other components is 0. Therefore, the method provided in this application can also be applied to the calculation of the thermophysical properties of pure substances.

[0385] In some embodiments, the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid composed of each of the two components in the gasification fluid are calculated based on the following formulas:

[0386]

[0387]

[0388]

[0389]

[0390]

[0391] In the formula,

[0392] , , , , These are the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid composed of pure working fluid components i and j, respectively.

[0393] , , , , These are the critical temperature, critical pressure, eccentricity factor, contrast dipole moment, and contrast de Broglie wavelength of pure working fluid component i, respectively.

[0394] , , , , These are the critical temperature, critical pressure, eccentricity factor, contrast dipole moment, and contrast de Broglie wavelength of the pure working fluid component j, respectively.

[0395] k ij The interaction coefficient k is the interaction coefficient when pure working fluid component i and pure working fluid component j form a mixed working fluid. ij The specific values ​​are shown in Table 1 below.

[0396] Table 1. Values ​​of the interaction coefficient

[0397]

[0398] In some embodiments, the cross-second virial coefficient of the mixed working fluid composed of each of the two said components is calculated based on the following formula:

[0399]

[0400] In the formula,

[0401] The comparative second virial coefficient is the coefficient of the mixed working fluid composed of pure working fluid components i and j.

[0402] The cross-second virial coefficient represents the coefficient of the mixture of working fluids composed of pure working fluid components i and j.

[0403] This represents the critical pressure of the mixture of a working fluid composed of pure working fluid components i and j.

[0404] This represents the mixing critical temperature of a mixed working fluid composed of pure working fluid components i and j.

[0405] R represents the universal gas constant, with a specific value of . ;

[0406] , These respectively represent the simple spherical term, nonpolar term, and quantum term in the second virial coefficients as a function of the comparison temperature. A function relating change; , , The calculation formula is given in the foregoing embodiments;

[0407] This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment The function relating the changes; see the foregoing examples for the function relating the polarity term in the second virial coefficient to the relative temperature and the relative dipole moment.

[0408] This represents the relative temperature of the mixed working fluid composed of pure working fluid components i and j. T represents the temperature in the state parameters of the gasified substance;

[0409] The mixing eccentricity factor represents the mixture of the working fluid composed of pure working fluid components i and j.

[0410] This represents the mixed contrast dipole moment of a mixed working fluid composed of pure working fluid components i and j;

[0411] The wavelength represents the mixed-contrast de Broglie wavelength of a mixed working medium composed of pure working medium components i and j.

[0412] In some embodiments, the second virial coefficient of the gasified substance is calculated based on the following formula:

[0413]

[0414] In the formula,

[0415] This represents the second virial coefficient of the gasified substance;

[0416] , These represent the mole fractions of pure working fluid components i and j in the mixed working fluid, respectively.

[0417] The cross-second virial coefficient represents the coefficient of the mixture of working fluids composed of pure working fluid components i and j.

[0418] n represents the number of pure working substances in the gasification process.

[0419] In some embodiments, the third-dimensional coefficient of the gasified substance is calculated based on the following formula:

[0420]

[0421]

[0422] In the formula,

[0423] The cross-third virial coefficient represents the coefficient of a mixed working fluid composed of pure working fluid components i, j, and k.

[0424] , , Let i, j, and k represent the third-dimensional coefficients of the pure working fluid components i, j, and k, respectively.

[0425] This represents the third-dimensional coefficient of the gasified substance;

[0426] , , These represent the mole fractions of the pure working fluid components i, j, and k in the mixed working fluid, respectively.

[0427] n represents the number of pure working substances in the gasification process.

[0428] In some embodiments, the density of the gasified substance is calculated iteratively using the following formula:

[0429]

[0430] In the formula,

[0431] ρ represents the density of the gasified substance;

[0432] T represents the temperature in the state parameters of the gasification substance;

[0433] p represents the pressure in the state parameters of the gaseous substance;

[0434] R represents the universal gas constant;

[0435] This represents the second virial coefficient of the gasified substance;

[0436] The third-dimensional coefficient of the gasified substance is represented.

[0437] Specifically, substituting T and p... Density ρ is obtained through iterative calculation.

[0438] In some embodiments, the thermodynamic properties include residual internal energy, which is calculated according to the following formula:

[0439]

[0440] In the formula,

[0441] This represents the remaining internal energy of the gasified substance;

[0442] R represents the universal gas constant;

[0443] T represents the temperature in the gasification state parameters;

[0444] This represents the second virial coefficient of the gasified substance;

[0445] This represents the third-dimensional coefficient of the gasified substance;

[0446] ρ represents the density of the gasified substance.

[0447] In some embodiments, the thermodynamic property includes internal energy, which is calculated according to the following formula:

[0448]

[0449]

[0450]

[0451]

[0452] In the formula,

[0453] This represents the internal energy of the gasified substance;

[0454] This represents the remaining internal energy of the gasified substance;

[0455] This represents the ideal internal energy of the gasified substance;

[0456] This refers to the temperature in the state parameters of the gasified substance;

[0457] This indicates the density of the gasified substance;

[0458] This represents the specific heat capacity at constant volume of an ideal gas in a gaseous chemical process.

[0459] This represents the specific heat capacity at constant pressure of an ideal gas.

[0460] Represents the universal gas constant;

[0461] n and m represent The number of different types of related items;

[0462] , , , express The specific parameters of the related items are shown in Table 2 below.

[0463] Table 2 Specific parameters of related terms

[0464]

[0465] In some embodiments, the thermodynamic property includes residual enthalpy, which is calculated according to the following formula:

[0466]

[0467] In the formula,

[0468] This indicates the residual enthalpy of the gasified substance;

[0469] R represents the universal gas constant;

[0470] T represents the temperature in the gasification state parameters;

[0471] This represents the second virial coefficient of the gasified substance;

[0472] This represents the third-dimensional coefficient of the gasified substance;

[0473] ρ represents the density of the gasified substance.

[0474] In some embodiments, the thermodynamic property includes enthalpy, which is calculated according to the following formula:

[0475]

[0476]

[0477] In the formula,

[0478] This represents the enthalpy of the gasified substance;

[0479] This indicates the residual enthalpy of the gasified substance;

[0480] This represents the ideal enthalpy of the gasified substance;

[0481] This refers to the temperature in the state parameters of the gasified substance;

[0482] This indicates the density of the gasified substance;

[0483] The ideal gas specific heat capacity at constant pressure represents the gaseous chemical substance. For the specific calculation formula, please refer to the aforementioned examples.

[0484] In some embodiments, the thermodynamic property includes residual entropy, which is calculated according to the following formula:

[0485]

[0486] In the formula,

[0487] This represents the residual entropy of the gasified substance;

[0488] R represents the universal gas constant;

[0489] T represents the temperature in the gasification state parameters;

[0490] This represents the second virial coefficient of the gasified substance;

[0491] This represents the third-dimensional coefficient of the gasified substance;

[0492] ρ represents the density of the gasified substance.

[0493] In some embodiments, the thermodynamic property includes entropy, which is calculated according to the following formula:

[0494]

[0495]

[0496] In the formula,

[0497] This represents the entropy of the gasified substance;

[0498] This represents the residual entropy of the gasified substance;

[0499] This represents the ideal entropy of the gasified substance;

[0500] Indicates reference state , The ideal entropy of the gasified substance is taken as 0 J*mol. -1 *K -1 ;

[0501] This represents the density of an ideal gaseous chemical substance under reference conditions. ;

[0502] Indicates the temperature under reference conditions;

[0503] Indicates the pressure under reference conditions;

[0504] The ideal gas specific heat capacity at constant pressure represents the gaseous chemical substance; the specific calculation formula is given in the aforementioned embodiments.

[0505] T represents the temperature in the gasification state parameters;

[0506] ρ represents the density of the gasified substance;

[0507] R represents the universal gas constant.

[0508] In some embodiments, the thermodynamic properties include residual specific heat at constant volume, which is calculated according to the following formula:

[0509]

[0510] In the formula,

[0511] This represents the residual specific heat at constant volume of the gasified substance;

[0512] R represents the universal gas constant;

[0513] T represents the temperature in the gasification state parameters;

[0514] This represents the second virial coefficient of the gasified substance;

[0515] This represents the third-dimensional coefficient of the gasified substance;

[0516] ρ represents the density of the gasified substance.

[0517] In some embodiments, the thermodynamic property includes specific heat at constant volume, which is calculated according to the following formula:

[0518]

[0519]

[0520] In the formula,

[0521] This represents the specific heat at constant volume of the gasified substance;

[0522] This represents the residual specific heat at constant volume of the gasified substance;

[0523] This represents the ideal isochoric specific heat of the gasified substance;

[0524] R represents the universal gas constant;

[0525] The ideal gas specific heat capacity at constant pressure represents the gaseous chemical substance. For the specific calculation formula, please refer to the aforementioned examples.

[0526] In some embodiments, the thermodynamic property includes residual isobaric specific heat, which is calculated according to the following formula:

[0527]

[0528]

[0529]

[0530] In the formula,

[0531] This represents the residual specific heat at constant pressure of the gasified substance;

[0532] This represents the residual specific heat at constant volume of the gasified substance;

[0533] R represents the universal gas constant;

[0534] T represents the temperature in the gasification state parameters;

[0535] This indicates the pressure in the state parameters of the gasified substance;

[0536] This represents the second virial coefficient of the gasified substance;

[0537] This represents the third-dimensional coefficient of the gasified substance;

[0538] ρ represents the density of the gasified substance.

[0539] In some embodiments, the thermodynamic property includes isobaric specific heat, which is calculated according to the following formula:

[0540]

[0541] In the formula,

[0542] This indicates the specific heat at constant pressure of the gasified substance;

[0543] This represents the residual specific heat at constant pressure of the gasified substance;

[0544] The specific gas heat capacity at constant pressure represents the ideal gas heat capacity of the gasified substance. For the specific calculation method, please refer to the aforementioned examples.

[0545] In some embodiments, the thermodynamic property includes the speed of sound, which is calculated according to the following formula:

[0546]

[0547]

[0548]

[0549]

[0550] In the formula,

[0551] w represents the speed of sound of the gasified substance;

[0552] R represents the universal gas constant;

[0553] T represents the temperature in the gasification state parameters;

[0554] This indicates the ideal specific heat ratio of the gasified substance;

[0555] This indicates the relative molecular mass of the gasified chemical substance;

[0556] This represents the second virial coefficient of the speed of sound;

[0557] This represents the third-dimensional coefficient of the speed of sound;

[0558] ρ represents the density of the gasified substance;

[0559] The ideal gas specific heat capacity at constant pressure represents the gaseous chemical substance; the specific calculation formula is given in the aforementioned embodiments.

[0560] The ideal gas specific heat capacity at constant volume represents the gaseous chemical substance; the specific calculation formula is given in the aforementioned embodiments.

[0561] This represents the second virial coefficient of the gasified substance;

[0562] The third-dimensional coefficient of the gasified substance is represented.

[0563] In some embodiments, the rarefied gas transport properties of the gasified substance are calculated according to the following formula:

[0564]

[0565]

[0566]

[0567] In the formula,

[0568] , These represent the rarefied gas transport properties of pure working fluid components i and j at temperature T, and can represent viscosity η or thermal conductivity λ.

[0569] T represents the temperature in the gasification state parameters;

[0570] These are parameters representing the transport properties of rarefied gases that are specific to fluids.

[0571] This indicates the rarefied gas transport properties of a mixed gaseous chemical substance;

[0572] , These represent the mole fractions of pure working fluid components i and j in the mixed working fluid, respectively.

[0573] n represents the number of pure working substances in the gasification process;

[0574] The factor representing the influence of the mixture of component i and component j on transport properties;

[0575] , These represent the relative molecular masses of components i and j, respectively.

[0576] Fluid-specific rarefied gas transport properties parameters The values ​​of are shown in Table 3.

[0577] Table 3. Fluid-specific rarefied gas transport properties parameters The value of

[0578]

[0579] In some embodiments,

[0580] The actual transport properties of the gasified substance are calculated using the following formula:

[0581]

[0582]

[0583]

[0584] In the formula,

[0585] X represents the actual transport properties of the gaseous substance, which can represent viscosity η or thermal conductivity λ.

[0586] This indicates the rarefied gas transport properties of a mixed gaseous chemical substance;

[0587] It is the dimensionless residual entropy;

[0588] These are fluid-specific residual transport property parameters. Represents the i-th type of element parameter;

[0589] Represents the mole fraction of the i-th component;

[0590] This represents the residual entropy of the gasified substance;

[0591] This refers to the temperature in the state parameters of the gasified substance;

[0592] This indicates the density of the gasified substance;

[0593] R represents the universal gas constant.

[0594] Table 4. Fluid-specific residual transport property parameters Specific value

[0595]

[0596] The method provided in this application innovatively combines the virial equation and the residual entropy scaling method to construct a thermophysical property calculation method applicable to gasification systems such as IGCC. This method achieves unified closed-loop calculations of density, thermodynamic properties, and transport properties, exhibiting high engineering adaptability. Furthermore, it proposes a modular thermophysical property calculation framework for complex gasification refrigerants: for typical gasification refrigerants such as CO, CO2, H2, H2O, CH4, N2, and O2, and their combinations, a set of calculation methods adapted to their thermophysical property variation patterns has been established, particularly suitable for rapid thermophysical property calculations under multi-component variable operating conditions. It can output multiple property data covering density, specific heat, enthalpy, entropy, sound velocity, viscosity, and thermal conductivity, providing one-stop data support for IGCC system modeling, thermodynamic process simulation, and optimization, significantly improving the accuracy and efficiency of system simulation. It is particularly suitable for calculating the thermophysical properties of syngas and its combustion products in integrated gasification combined cycle (IGCC) systems.

[0597] In summary, the method provided in this application can significantly improve the accuracy and reliability of calculating the thermophysical properties of gasified substances and their mixtures, especially under conditions where experimental data is scarce, such as high temperature and high pressure, and has strong computational extrapolation capabilities. Furthermore, the method provided in this application has a simple and efficient calculation process, requires few calculation parameters, and has a fast calculation speed, making it easy to quickly promote and apply in practical engineering and simulation analysis.

[0598] See Figures 2 to 4 As shown, the calculation results of the method provided in this application embodiment are less than 5% different from existing experimental data after verification under actual working conditions. This method can provide accurate thermophysical data support for integrated gasification combined cycle (IGCC) systems and other related fields.

[0599] Based on the same inventive concept, this application also provides a gasification thermophysical property calculation device based on the virial equation and the residual entropy scaling method.

[0600] Figure 5 This is a schematic diagram of a gasification thermophysical property calculation device based on the virial equation and the residual entropy scaling method provided in an embodiment of this application. Figure 5 As shown, the device includes:

[0601] The first calculation module 21 is used to calculate the comparative second virial coefficient and the comparative third virial coefficient of each component based on the state parameters of the gasified substance and the physical property parameters of each component.

[0602] The second calculation module 22 is used to calculate the second virial coefficient and the third virial coefficient of the gasified substance using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second virial coefficient and the comparative third virial coefficient of each component.

[0603] The third calculation module 23 is used to calculate the density of the gasified substance using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance.

[0604] The fourth calculation module 24 is used to calculate the thermodynamic properties of the gasified substance based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include residual entropy;

[0605] The fifth calculation module 25 is used to calculate the rarefied gas transport properties of the gasified substance based on the physical property parameters and state parameters of each component in the gasified substance.

[0606] The sixth calculation module 26 is used to calculate the transport properties of the gasified substance using the residual entropy scaling method, based on the residual entropy and the transport properties of the rarefied gas.

[0607] The gaseous precipitate thermophysical property calculation device based on the virial equation and the residual entropy scaling method provided in this application combines the virial equation and the residual entropy scaling method to achieve unified closed-loop calculation of density-thermodynamic properties-transport properties. It has high engineering adaptability and can be used for thermophysical property calculation of gaseous precipitates with complex components. It can significantly improve the accuracy and reliability of thermophysical property calculation of gaseous precipitates, especially under conditions where experimental data is scarce, such as high temperature and high pressure, it has strong computational extrapolation capabilities.

[0608] The embodiments of the apparatus provided in this application can be used to execute the processing flow of the above method embodiments, and will not be repeated here. Please refer to the detailed description of the above method embodiments.

[0609] Figure 6 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of this application, as shown below. Figure 6As shown, the electronic device may include a processor 301, a communications interface 302, a memory 303, and a communication bus 304, wherein the processor 301, the communications interface 302, and the memory 303 communicate with each other via the communication bus 304. The processor 301 may call logical instructions in the memory 303 to execute the methods described in any of the above embodiments.

[0610] Furthermore, the logical instructions in the aforementioned memory 303 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0611] This embodiment discloses a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer can perform the methods provided in the above-described method embodiments.

[0612] This embodiment provides a computer-readable storage medium storing a computer program that causes the computer to perform the methods provided in the above-described method embodiments.

[0613] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0614] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0615] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0616] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0617] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0618] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for calculating the thermophysical properties of gasification processes based on the virial equation and the residual entropy scaling method, characterized in that, include: Based on the state parameters of the gasified substance and the physical properties of each component, the comparative second virial coefficient and comparative third virial coefficient of each component are calculated. The second and third virial coefficients of the gasified substance are calculated using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second and third virial coefficients of each component. The density of the gasified substance is calculated using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance. The thermodynamic properties of the gasified substance are calculated based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include the residual entropy. Based on the physical properties and state parameters of each component in the gasified substance, the rarefied gas transport properties of the gasified substance are calculated. The transport properties of the gasified substance are calculated using the residual entropy scaling method, based on the residual entropy and the transport properties of the rarefied gas.

2. The method according to claim 1, characterized in that, For components in the gasified substance that are simple spherical fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas: In the formula, This indicates the comparison of the second virial coefficient; This indicates the comparison of the third dimensional coefficient; This indicates that the simple spherical term in the second virial coefficient varies with the comparison temperature. A function relating change; This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

3. The method according to claim 1, characterized in that, For components in the gasified substance that are non-polar fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas: In the formula, This indicates the comparison of the second virial coefficient; This indicates the comparison of the third dimensional coefficient; , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change; This represents the eccentricity factor of the component; This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change; , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

4. The method according to claim 1, characterized in that, For the components in the gasified substance that are polar fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formulas: In the formula, This indicates the comparison of the second virial coefficient; This indicates the comparison of the third dimensional coefficient; , These respectively represent the simple spherical term and the nonpolar term in the second virial coefficients as a function of the comparison temperature. A function relating change; This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment A function relating change; This represents the eccentricity factor of the component; This represents the contrast dipole moment of the component; This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; This indicates that the polarity term in the third virial coefficient of a polar fluid varies with the corresponding temperature. Eccentricity factor Contrast dipole moment A function relating change; , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component.

5. The method according to claim 1, characterized in that, For the components in the gasified substance that are quantum fluids, the comparative second virial coefficient and comparative third virial coefficient of the component are calculated according to the following formula: In the formula, This indicates the comparison of the second virial coefficient; This indicates the comparison of the third dimensional coefficient; , This indicates that the simple spherical and quantum terms in the third virial coefficients vary with the comparison temperature. A function relating change; , Temperature represents the state parameters of a gaseous substance. This indicates the critical temperature of the component. This indicates the contrastive de Broglie wavelength of the component; , These respectively represent the simple spherical term and the quantum term in the second virial coefficient as a function of the comparison temperature. A function relating change.

6. The method according to claim 1, characterized in that, For carbon dioxide in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of carbon dioxide are calculated according to the following formulas: In the formula, The second virial coefficient representing the contrast of carbon dioxide; The third virial coefficient representing the contrast of carbon dioxide; This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; This indicates that the nonpolar term in the third virial coefficient of a nonpolar fluid varies with the corresponding temperature. Eccentricity factor A function relating change; , Temperature represents the state parameters of a gaseous substance. Indicates the critical temperature of carbon dioxide; The eccentricity factor represents carbon dioxide.

7. The method according to claim 1, characterized in that, For water in the gasified substance, the comparative second virial coefficient and comparative third virial coefficient of water are calculated according to the following formulas: In the formula, The second virial coefficient representing the contrast of water; The third virial coefficient representing the contrast of water; This indicates that the simple spherical term in the third virial coefficient varies with the comparison temperature. A function relating change; , Temperature represents the state parameters of a gaseous substance. Indicates the critical temperature of water; The eccentricity factor representing water; This represents the contrast dipole moment of water.

8. The method according to claim 1, characterized in that, The calculation of the second and third virial coefficients of the gasified substance using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second and third virial coefficients of each component includes: Based on the critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength, and interaction coefficient of each component in the gasified propellant, the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed propellant composed of each pair of components are calculated. Based on the temperature of the gasified substance and the mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working substance composed of each of the two components, calculate the cross second virial coefficient of the mixed working substance composed of each of the two components. The second virial coefficient of the gasified substance is calculated based on the cross-second virial coefficient of the mixed working substance composed of each of the two components in the gasified substance and the mole fraction of each component in the gasified substance. Based on the comparative third virial coefficient of each of the three components in the gasified working fluid, the cross third virial coefficient of the mixed working fluid composed of the three components is calculated. The third dimensional coefficient of the gasified substance is calculated based on the cross-third dimensional coefficient of the mixed working substance composed of three components in each gasified substance and the mole fraction of each component in the gasified substance.

9. The method according to claim 8, characterized in that, The mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid composed of each of the two components in the gasification fluid are calculated based on the following formulas: In the formula, , , , , Each is composed of pure working fluid components , The mixing critical temperature, mixing critical pressure, mixing eccentricity factor, mixing contrast dipole moment, and mixing contrast de Broglie wavelength of the mixed working fluid. , , , , The components are pure working fluids. Critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength; , , , , The components are pure working fluids. Critical temperature, critical pressure, eccentricity factor, contrast dipole moment, contrast de Broglie wavelength; pure working fluid component With pure working fluid components The interaction coefficient when the working fluid is mixed.

10. The method according to claim 8, characterized in that, The cross-second virial coefficient of each of the two components in the mixed working fluid is calculated based on the following formula: In the formula, pure working fluid component , The comparative second virial coefficient of the mixed working fluid; Indicates a composition of pure working fluid elements , The cross-second virial coefficient of the mixed working fluid; Indicates a composition of pure working fluid elements , The critical pressure of the mixture of working fluids; Indicates a composition of pure working fluid elements , The critical mixing temperature of the mixed working fluid; Represents the universal gas constant; , , These respectively represent the simple spherical term, nonpolar term, and quantum term in the second virial coefficients as a function of the comparison temperature. A function relating change; This indicates that the polarity term in the second virial coefficient varies with the comparison temperature. and contrast dipole moment A function relating change; Indicates a composition of pure working fluid elements , The relative temperatures of the mixed working fluids. , Temperature represents the state parameters of a gaseous substance; Indicates a composition of pure working fluid elements , The mixing eccentricity factor of the mixed working fluid; Indicates a composition of pure working fluid elements , The mixed contrast dipole moment of the mixed working fluid; Indicates a composition of pure working fluid elements , The mixing of the working fluids is compared with the de Broglie wavelength.

11. The method according to claim 8, characterized in that, The second virial coefficient of the gasified substance is calculated based on the following formula: In the formula, This represents the second virial coefficient of the gasified substance; , They represent the pure working fluid components in the mixed working fluid. , Their respective mole fractions; Indicates a composition of pure working fluid elements , The cross-second virial coefficient of the mixed working fluid; This indicates the number of pure working fluid components in the gasified chemical substance.

12. The method according to claim 8, characterized in that, The third-dimensional coefficient of the gasified substance is calculated based on the following formula: In the formula, Indicates a composition of pure working fluid elements , , The cross-third virial coefficient of the mixed working fluid; , , They represent the components of the pure working fluid, respectively. , , The coefficients in the third dimension; This represents the third-dimensional coefficient of the gasified substance; , , They represent the pure working fluid components in the mixed working fluid. , , Their respective mole fractions; This indicates the number of pure working fluid components in the gasified chemical substance.

13. The method according to claim 1, characterized in that, The density of the gasified substance is calculated iteratively using the following formula: In the formula, This indicates the density of the gasified substance; Temperature represents the state parameters of a gaseous substance; This represents the pressure in the state parameters of a gaseous substance. Represents the universal gas constant; This represents the second virial coefficient of the gasified substance; The third-dimensional coefficient of the gasified substance is represented.

14. The method according to claim 1, characterized in that, The thermodynamic properties include residual internal energy, which is calculated using the following formula: In the formula, This represents the remaining internal energy of the gasified substance; Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This represents the second virial coefficient of the gasified substance; This represents the third-dimensional coefficient of the gasified substance; This indicates the density of the gasified chemical substance.

15. The method according to claim 14, characterized in that, The thermodynamic properties include internal energy, which is calculated using the following formula: In the formula, This represents the internal energy of the gasified substance; This represents the remaining internal energy of the gasified substance; This represents the ideal internal energy of the gasified substance; This refers to the temperature among the state parameters of the gasified substance; This indicates the density of the gasified substance; This represents the specific heat capacity at constant volume of an ideal gas in a gaseous chemical process. This represents the specific heat capacity of an ideal gas at constant pressure. Represents the universal gas constant; , express The number of different types of related items; , , , express The parameters of the related items.

16. The method according to claim 1, characterized in that, The thermodynamic properties include residual enthalpy, which is calculated using the following formula: In the formula, This indicates the residual enthalpy of the gasified substance; Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This represents the second virial coefficient of the gasified substance; This represents the third-dimensional coefficient of the gasified substance; This indicates the density of the gasified chemical substance.

17. The method according to claim 16, characterized in that, The thermodynamic property includes enthalpy, which is calculated using the following formula: In the formula, This represents the enthalpy of the gasified substance; This indicates the residual enthalpy of the gasified substance; This represents the ideal enthalpy of the gasified substance; This refers to the temperature among the state parameters of the gasified substance; This indicates the density of the gasified substance; This represents the ideal gas specific heat capacity at constant pressure for gasification.

18. The method according to claim 1, characterized in that, The thermodynamic properties include residual entropy, which is calculated using the following formula: In the formula, This represents the residual entropy of the gasified substance; Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This represents the second virial coefficient of the gasified substance; This represents the third-dimensional coefficient of the gasified substance; This indicates the density of the gasified chemical substance.

19. The method according to claim 18, characterized in that, The thermodynamic property includes entropy, which is calculated using the following formula: In the formula, This represents the entropy of the gasified substance; This represents the residual entropy of the gasified substance; This represents the ideal entropy of the gasified substance; Indicates reference state , The ideal entropy of the gasified substance is taken as ; This represents the density of an ideal gaseous chemical substance under reference conditions. ; Indicates the temperature under reference conditions; Indicates the pressure under reference conditions; This represents the specific heat capacity at constant pressure of an ideal gas in a gaseous chemical process. This refers to the temperature among the state parameters of the gasified substance; This indicates the density of the gasified substance; This represents the universal gas constant.

20. The method according to claim 1, characterized in that, The thermodynamic properties include residual specific heat at constant volume, which is calculated according to the following formula: In the formula, This represents the residual specific heat at constant volume of the gasified substance; Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This represents the second virial coefficient of the gasified substance; This represents the third-dimensional coefficient of the gasified substance; This indicates the density of the gasified chemical substance.

21. The method according to claim 20, characterized in that, The thermodynamic properties include specific heat at constant volume, which is calculated according to the following formula: In the formula, This indicates the specific heat at constant volume of the gasified substance; This represents the residual specific heat at constant volume of the gasified substance; This represents the ideal isochoric specific heat of the gasified substance; Represents the universal gas constant; This represents the ideal gas specific heat capacity at constant pressure for gasification.

22. The method according to claim 20, characterized in that, The thermodynamic properties include residual isobaric specific heat, which is calculated according to the following formula: In the formula, This represents the residual specific heat at constant pressure of the gasified substance; This represents the residual specific heat at constant volume of the gasified substance; Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This indicates the pressure in the state parameters of the gasified substance; This represents the second virial coefficient of the gasified substance; This represents the third-dimensional coefficient of the gasified substance; This indicates the density of the gasified chemical substance.

23. The method according to claim 22, characterized in that, The thermodynamic properties include specific heat at isobaric pressure, which is calculated according to the following formula: In the formula, This indicates the specific heat at constant pressure of the gasified substance; This represents the residual specific heat at constant pressure of the gasified substance; This represents the ideal gas specific heat capacity at constant pressure for gasification.

24. The method according to claim 1, characterized in that, The thermodynamic property includes the speed of sound, which is calculated using the following formula: In the formula, The velocity of sound of the gasified substance is indicated. Represents the universal gas constant; This refers to the temperature among the state parameters of the gasified substance; This indicates the ideal specific heat ratio of the gasified substance; This indicates the relative molecular mass of the gasified chemical substance; This represents the second virial coefficient of the speed of sound; This represents the third-dimensional coefficient of the speed of sound; This indicates the density of the gasified substance; This represents the specific heat capacity at constant pressure of an ideal gas in a gaseous chemical process. This represents the specific heat capacity at constant volume of an ideal gas in a gaseous chemical process. This represents the second virial coefficient of the gasified substance; The third-dimensional coefficient of the gasified substance is represented.

25. The method according to claim 1, characterized in that, The rarefied gas transport properties of the described gasification substance are calculated using the following formula: In the formula, , These represent the rarefied gas transport properties of pure working fluid components i and j at temperature T, including viscosity η or thermal conductivity λ. T represents the temperature in the state parameters of the gasified substance; These are parameters representing the transport properties of rarefied gases that are specific to fluids. This indicates the rarefied gas transport properties of a mixed gaseous chemical substance; , These represent the mole fractions of pure working fluid components i and j in the mixed working fluid, respectively. n represents the number of pure working substances in the gasification process; The factor representing the influence of the mixture of component i and component j on transport properties; , These represent the relative molecular masses of components i and j, respectively.

26. The method according to claim 1, characterized in that, The actual transport properties of the gasified substance are calculated using the following formula: In the formula, X represents the actual transport properties of the gasified substance; This indicates the rarefied gas transport properties of a mixed gaseous chemical substance; It is the dimensionless residual entropy; These are fluid-specific residual transport property parameters. Represents the i-th type of element parameter; Represents the mole fraction of the i-th component; This represents the residual entropy of the gasified substance; This refers to the temperature among the state parameters of the gasified substance; This indicates the density of the gasified substance; R represents the universal gas constant.

27. A device for calculating the thermophysical properties of gasification processes based on the virial equation and the residual entropy scaling method, characterized in that, include: The first calculation module is used to calculate the comparative second virial coefficient and the comparative third virial coefficient of each component based on the state parameters of the gasified substance and the physical property parameters of each component. The second calculation module is used to calculate the second virial coefficient and the third virial coefficient of the gasified substance using the mixing rules based on the state parameters, the physical property parameters of each component, and the comparative second virial coefficient and the comparative third virial coefficient of each component. The third calculation module is used to calculate the density of the gasified substance using the virial equation based on the state parameters and the second and third virial coefficients of the gasified substance. The fourth calculation module is used to calculate the thermodynamic properties of the gasified substance based on the state parameters, the density of the gasified substance, and the second and third virial coefficients of the gasified substance, wherein the thermodynamic properties include residual entropy; The fifth calculation module is used to calculate the rarefied gas transport properties of the gasified substance based on the physical properties and state parameters of each component in the gasified substance. The sixth calculation module is used to calculate the transport properties of the gasified substance using the residual entropy scaling method, based on the residual entropy and the transport properties of the rarefied gas.

28. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-26.

29. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-26.

Images