A method for calculating interfacial Gibbs free energy in microinterface systems

Abstract

The present invention provides a method for calculating the interfacial Gibbs free energy in a microinterface system, comprising the following steps: (A) establishing a Gibbs free energy equation for gas dissolution in a solution; (B) establishing a chemical equation for gas dissolution in a solution; (C) obtaining the Henry coefficient based on the equivalence principle between the equilibrium constant and the Henry coefficient; and (D) establishing a relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer in the microinterface system. The calculation method of the present invention is dedicated to exploring interfacial effects and establishing a related control model. By fitting experimental data, a model of interfacial Gibbs free energy and mass transfer membrane thickness based on different operating conditions and liquid properties is established. The model provides a quantitative contribution of interface and size effects to optimize the design and operation of microinterface enhanced reactors.

Description

Technical Field

[0001] The present invention belongs to the field of micro-interface strengthening, and in particular to a method for calculating interface Gibbs free energy in a micro-interface system. Background Art

[0002] In recent years, many new technologies have been developed to enhance contact between gas and liquid phases, such as introducing disturbances into multiphase flows and applying electric fields. Bubble columns, with their advantages of simple structure, ease of operation, and excellent heat transfer, have been widely used in oil refining, pharmaceuticals, material synthesis, water treatment, and fine chemicals. In bubble columns, the high dispersion of gas in the liquid phase results in a large gas-liquid contact area, which improves mass transfer efficiency to a certain extent. Therefore, a bubble column reactor (BCR) is often used as the reaction device for chemical absorption of alkaline solutions. Researchers used ammonia as the adsorbent and conducted single-factor experiments in a BCR, determining the relationship between adsorbent concentration, gas volume, and adsorption capacity. Taborda et al. proposed a bubble motion dynamics model based on random generation of eccentricity and motion angle, and studied the bubble dynamics and mass transfer behavior of carbon dioxide absorption by sodium hydroxide in a BCR.

[0003] However, the bubbles in conventional BCRs are typically only millimeter-sized, resulting in a generally low gas holdup and interfacial area. At a given gas-liquid flow rate, the size and distribution uniformity of the bubbles in the BCR significantly affect the gas holdup and gas-liquid interfacial area, which in turn affects the macroscopic reaction rate. Microbubbles (less than 1.0 mm in diameter) have attracted widespread attention in industrial processes due to their excellent performance in gas-liquid mass transfer efficiency. Currently, microbubbles have been successfully generated using membranes, microfluidics, and Venturi bubble generators. Compared to millimeter-sized macrobubbles, microbubbles are widely used in chemical absorption, wastewater treatment, battery preparation, and other fields due to their increased interfacial area, thus exhibiting a good enhancement effect.

[0004] Microinterface Enhanced Reactors / Reactions (MIR) and microinterface mass transfer enhancement are characterized by the ability to form a complete MIR system within the reactor under high-throughput conditions. This makes it suitable for large-capacity reaction units with annual production capacities ranging from 100,000 to 1,000,000 tons. MIR technology significantly improves mass transfer rates and macroscopic reaction rates, eliminating the need for new reactor construction and minimizing modification costs. Therefore, the use of MIR technology to study gas dissolution is of great significance. Notably, due to the advantages of non-invasive technology such as high spatial resolution and no interference with fluid dynamics, the previously established online measurement and imaging system (OMIS) can accurately measure the size and distribution of microbubbles in MIR systems, thereby effectively characterizing multiphase flow. Furthermore, experiments have revealed the presence of a thick interface layer on the surface of microbubbles, a previously overlooked feature. Therefore, exploring interfacial effects and establishing relevant regulatory models is a highly significant research topic.

[0005] In view of this, the present invention is proposed. Summary of the Invention

[0006] In view of this, the present invention provides a method for calculating the interfacial Gibbs free energy in a microinterface system to explore the influence of bubble size on the interface aspects of the microinterface system. By fitting experimental data, a model of interfacial Gibbs free energy and mass transfer membrane thickness based on different operating conditions and liquid properties is established. The quantitative contribution of interface and size effects is given through model calculation to optimize the design and operation of the microinterface enhanced reactor.

[0007] In order to achieve the above-mentioned purpose of the present invention, the present invention adopts the following technical solutions:

[0008] (A) Establish the Gibbs free energy equation for gas dissolution in solution:

[0009] The Gibbs free energy of gas dissolved in solution in a microinterface system is expressed as the sum of bulk Gibbs free energy, surface Gibbs free energy and interface Gibbs free energy, which can be expressed as follows:

[0010] (1)

[0011] Where G total is the Gibbs free energy of gas dissolution in solution, J / mol; G bulk is the bulk Gibbs free energy, J / mol; G surface is the surface Gibbs free energy, J / mol; G interface is the interfacial Gibbs free energy in the microinterface system, J / mol;

[0012] (B) Create a chemical equation for the dissolution of a gas in a solution:

[0013] Among them, the dissolution of gas includes the following chemical equation:

[0014] (2)

[0015] The equilibrium constant of the gas dissolution reaction is expressed as:

[0016] (3)

[0017] Among them, G g is the Gibbs free energy of the gas state, J / mol, R is the universal gas constant, J / mol·K, and T is the absolute temperature, K;

[0018] (C) According to the equivalence principle between equilibrium constant and Henry's constant, the Henry's constant is obtained;

[0019] Among them, in the traditional conventional bubble column system, the Henry coefficient is:

[0020] (4)

[0021] The Henry coefficient in the micro-interface system is:

[0022] (5)

[0023] Right now:

[0024] (6)

[0025] (7)

[0026] Combining formula (6) and formula (7) we get:

[0027] (8)

[0028] Substituting equation (1) into equation (8), we can obtain:

[0029] (9)

[0030] Since the liquid film consists of an inner layer and an outer layer, the surface Gibbs free energy can be expressed as:

[0031] (10)

[0032] in, δ M is the thickness of the mass transfer boundary layer, m; is the surface tension of the inner surface, is the surface tension of the outer layer, N / m; V m is the molar volume, m 3 / mol;

[0033] Since the surface tension of the inner and outer layers can be considered to be approximately equal, formula (10) can be simplified to obtain formula (11):

[0034] (11)

[0035] Where γ is the surface tension;

[0036] Combining formula (9) to formula (11), we can get formula (12):

[0037] (12)

[0038] (D) The relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer in the micro-interface system is established:

[0039] According to formula (12), the relationship between the interfacial Gibbs free energy of gas and the thickness of the mass transfer boundary layer is:

[0040] (13)

[0041] in, is the interfacial Gibbs free energy in the microinterface system.

[0042] In the calculation method of the present invention, it can be seen from formula (13) that as the mass transfer boundary thickness increases, the boundary layer thickness increases. δ M As the bubble diameter increases, the interface effect increases. G interface The value decreases.

[0043] In the calculation method of the present invention, the relationship between the interfacial Gibbs free energy and the Gibbs free energy in the solution is first obtained by establishing a Gibbs free energy equation for gas dissolution in a solution. Then, a chemical equation for gas dissolution in a solution is established to obtain the equilibrium constant of the gas dissolution reaction. Based on the equivalence principle of the equilibrium constant and the Henry coefficient, the Henry coefficient is calculated. Since the liquid film includes an inner layer and an outer layer, but the surface tensions of the inner and outer layers can be considered to be approximately equal, a calculation formula for the interfacial Gibbs free energy, the mass transfer boundary layer thickness, and the surface tension can be obtained.

[0044] The present invention also relates to a micro-interface enhanced reactor designed using the aforementioned calculation method. The micro-interface enhanced reactor designed using the aforementioned calculation method is more suitable for practical applications and can control microbubble size to an optimal state, thereby achieving a good micro-interface reaction effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Various other advantages and benefits will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiment below. The accompanying drawings are for illustration purposes only and are not to be considered as limiting the present invention. The same reference symbols are used throughout the drawings to represent the same components. In the drawings:

[0046] Figure 1 A schematic diagram of the distribution of carbon dioxide in a solution under the MIR system provided in an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the correlation between the interfacial Gibbs free energy and the mass transfer boundary layer thickness provided in an embodiment of the present invention;

[0048] Figure 3 The respective proportions of interface ideas and surface items provided for the embodiments of the present invention. DETAILED DESCRIPTION

[0049] The technical solutions of the present invention will be described clearly and completely below in conjunction with the accompanying drawings and specific embodiments. However, those skilled in the art will understand that the embodiments described below are only some embodiments of the present invention, not all embodiments, and are only used to illustrate the present invention and should not be regarded as limiting the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative work are within the scope of protection of the present invention.

[0050] The terms used in this disclosure are for the purpose of describing specific embodiments only and are not intended to limit the disclosure. As used in this disclosure and the appended claims, the singular forms "a," "an," "the," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items.

[0051] It should be understood that although the terms first, second, third, etc. may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from each other. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining."

[0052] In order to more clearly illustrate the technical solutions of the present invention, specific embodiments are provided below for illustration.

[0053] Example

[0054] The method for calculating the interfacial Gibbs free energy in a microinterface system includes the following steps:

[0055] (A) Establish the Gibbs free energy equation for gas dissolution in solution:

[0056] The Gibbs free energy of gas dissolved in solution in a microinterface system is expressed as the sum of bulk Gibbs free energy, surface Gibbs free energy and interface Gibbs free energy, which can be expressed as follows:

[0057] (1)

[0058] Where G total is the Gibbs free energy of gas dissolution in solution, J / mol; G bulk is the bulk Gibbs free energy, J / mol; G surfaceis the surface Gibbs free energy, J / mol; G interface is the interfacial Gibbs free energy in the microinterface system, J / mol;

[0059] (B) Create a chemical equation for the dissolution of a gas in a solution:

[0060] Among them, the dissolution of gas includes the following chemical equation:

[0061] (2)

[0062] The equilibrium constant of the gas dissolution reaction is expressed as:

[0063] (3)

[0064] Among them, G g is the Gibbs free energy of the gas state, J / mol, R is the universal gas constant, J / mol·K, and T is the absolute temperature, K;

[0065] (C) According to the equivalence principle between equilibrium constant and Henry's constant, the Henry's constant is obtained;

[0066] Among them, in the traditional conventional bubble column system, the Henry coefficient is:

[0067] (4)

[0068] The Henry coefficient in the micro-interface system is:

[0069] (5)

[0070] Right now:

[0071] (6)

[0072] (7)

[0073] Combining formula (6) and formula (7) we get:

[0074] (8)

[0075] Substituting equation (1) into equation (8), we can obtain:

[0076] (9)

[0077] Since the liquid film consists of an inner layer and an outer layer, the surface Gibbs free energy can be expressed as:

[0078] (10)

[0079] in, δ M is the thickness of the mass transfer boundary layer, m; is the surface tension of the inner surface, is the surface tension of the outer layer, N / m; V m is the molar volume, m 3 / mol;

[0080] Since the surface tension of the inner and outer layers can be considered to be approximately equal, formula (10) can be simplified to obtain formula (11):

[0081] (11)

[0082] Where γ is the surface tension;

[0083] Combining formula (9) to formula (11), we can get formula (12):

[0084] (12)

[0085] (D) The relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer in the micro-interface system is established:

[0086] According to formula (12), the relationship between the interfacial Gibbs free energy of gas and the thickness of the mass transfer boundary layer is:

[0087] (13)

[0088] in, is the interfacial Gibbs free energy in the microinterface system

[0089] In a specific embodiment, a method for calculating the interfacial Gibbs free energy in a microinterface system is studied for the reaction of sodium hydroxide absorbing carbon dioxide.

[0090] Among CO2 capture methods, chemical absorption using alkaline solutions is currently the most mature capture technology, offering advantages such as simple adsorbents and ease of large-scale application. In recent years, extensive research has been conducted on CO2 removal using various alkaline solutions, including ethanolamine (MEA), ammonia, and sodium carbonate. NaOH solutions, with CO2 removal rates reaching 92% to 99%, are widely used in coal-fired power plants, cement plants, and other fields due to their excellent adsorption properties. While CO2 reacts with sodium hydroxide at a high intrinsic reaction rate, CO2 suffers from low solubility and high mass transfer resistance. This low gas-liquid mass transfer rate also limits the macroscopic reaction rate. Therefore, improving this macroscopic reaction rate has been a key research focus and hot topic in this field.

[0091] In order to study the interfacial effect mechanism of sodium hydroxide absorbing carbon dioxide, Figure 1 As shown, the distribution diagram of carbon dioxide in the solution under the MIR system is obtained. Figure 1 According to classical thermodynamics, the Gibbs free energy of carbon dioxide in solution can be expressed as the sum of bulk free energy, surface Gibbs free energy, and interface Gibbs free energy. Therefore, the Gibbs free energy of carbon dioxide in this embodiment is also expressed as formula (1). The dissolution of carbon dioxide in this embodiment is expressed by the following chemical equation:

[0092] (14)

[0093] The physical properties of sodium hydroxide solutions of different concentrations at 298.15 K and 1 atm were recorded, and the following Table 1 was obtained;

[0094] Table 1: Physical properties of sodium hydroxide solutions at different concentrations at 298.15 K and 1 atm

[0095]

[0096] The amount of carbon dioxide absorbed by the sodium hydroxide in the carbon dioxide absorption reaction was recorded to obtain the following Table 2;

[0097] Table 2: Amount of carbon dioxide absorbed

[0098]

[0099] The saturated carbon dioxide concentration obtained after the experiment was recorded, as shown in Table 3 below;

[0100] Table 3: Saturated carbon dioxide concentration obtained from the experiment

[0101]

[0102] Note: vg = 0.0111 m / s, cNaOH = 0.3 mol / L, T = 298.15 K, vl = 0.0133 m / s.

[0103] As shown in formula (13), the surface tension is taken from Table 1, δ M 、 V m Taken from Table 2, H MIR / H bulk Obtained from Table 3, the calculation process is shown in Equation (15).

[0104] (15)

[0105] The predicted results of the interface and surface Gibbs free energy of microbubbles with different diameters are recorded and shown in Table 4 below;

[0106] Table 4 Prediction results of Gibbs free energy of microbubbles with different diameters

[0107]

[0108] Further research and regression were conducted on the relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer. The results are shown in Figure 2 As shown, the results show that ( G interface / ( γ * V m ) ) 1 / 3 and 1 / δ M There is a linear curve.

[0109] This shows that using γ and V to determine G interface This makes sense because as the mass transfer boundary layer thickness increases δ M As the bubble diameter increases, the interface effect increases. G interface The value decreases. Figure 2 The results shown can be obtained as follows:

[0110] (16)

[0111] The unit of the generalized constant 5.59 is m 2 .

[0112] In order to study the influence of MIR interface effect, the G interface to ( G interface + G surface ) and G surface to ( G interface + G surface ) ratio:

[0113] (17)

[0114] (18)

[0115] like Figure 3As shown in the figure, in conventional centimeter-scale BCRs, interface effects can be ignored due to their small proportion, but in MIRs, interface effects are not negligible. Although the interface proportion gradually decreases with increasing film thickness, it remains above 97% when the film thickness reaches 12 μm. This means that interface effects are dominant and must be considered in MIR systems.

[0116] Depend on Figure 1-3 The results show a linear relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer. As the thickness of the mass transfer boundary layer increases, the bubble diameter also increases, the interfacial effect increases, and the interfacial Gibbs free energy decreases. Although the proportion of the interface gradually decreases with increasing film thickness, it remains above 97% when the film thickness reaches 12 μm. This indicates that interfacial effects are dominant and must be considered in MIR systems.

[0117] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the interfacial Gibbs free energy in a microinterface system, characterized in that: include: (A) Establish the Gibbs free energy equation for gas dissolution in solution: The Gibbs free energy of gas dissolved in solution in a microinterface system is expressed as the sum of bulk Gibbs free energy, surface Gibbs free energy and interface Gibbs free energy, which can be expressed as follows: （1） Where G total is the Gibbs free energy of gas dissolution in solution, J / mol; G bulk is the bulk Gibbs free energy, J / mol; G surface is the surface Gibbs free energy, J / mol; G interface is the interfacial Gibbs free energy in the microinterface system, J / mol; (B) Create a chemical equation for the dissolution of a gas in a solution: Among them, the dissolution of gas includes the following chemical equation: （2） The equilibrium constant of the gas dissolution reaction is expressed as: （3） Among them, G g is the Gibbs free energy of the gas state, J / mol, R is the universal gas constant, J / mol·K, and T is the absolute temperature, K; (C) According to the equivalence principle between equilibrium constant and Henry's constant, the Henry's constant is obtained; Among them, in the traditional conventional bubble column system, the Henry coefficient is: （4） The Henry coefficient in the micro-interface system is: （5） Right now: （6） （7） Combining formula (6) and formula (7) we get: （8） Substituting equation (1) into equation (8), we can obtain: （9） Since the liquid film consists of an inner layer and an outer layer, the surface Gibbs free energy can be expressed as: （10） in, δ M is the thickness of the mass transfer boundary layer, m; is the surface tension of the inner surface, is the surface tension of the outer layer, N / m; V m is the molar volume, m 3 / mol; Since the surface tension of the inner and outer layers can be considered to be approximately equal, formula (10) can be simplified to obtain formula (11): （11） Where γ is the surface tension; Combining formula (9) to formula (11), we can get formula (12): （12） (D) The relationship between the interfacial Gibbs free energy and the thickness of the mass transfer boundary layer in the micro-interface system is established: According to formula (12), the relationship between the interfacial Gibbs free energy of gas and the thickness of the mass transfer boundary layer is: （13） in, is the interfacial Gibbs free energy in the microinterface system.

2. A micro-interface enhanced reactor designed using the calculation method of the interfacial Gibbs free energy under the micro-interface system described in claim 1.

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