CN109657406B - Modeling method of phase boundary area regulation model under MIHA pure pneumatic operation condition - Google Patents

Abstract

The invention relates to a modeling method of a phase boundary area regulation model under the MIHA pure pneumatic operation condition, which establishes an energy conversion model in a bubble breaker by analyzing a bubble generation process under the pure pneumatic condition; based on an energy conversion model and liquid circulation in the bubble breaker, calculating liquid flow, obtaining energy dissipation rate and bubble size of a gas-liquid intensive mixing area, and finally obtaining a phase boundary area calculation model. The method establishes a phase boundary area regulation model under the pure pneumatic operation condition aiming at the MIHA, comprehensively reflects the influence of the reactor structure, the physical properties and the operation parameters of the system and the input energy on the phase boundary area, and can realize the guidance on the reactor design and the reaction system design of the MIHA and the guidance on the design of the efficient reactor structure and the reaction system.

Description

Modeling method of phase interface area control model under pure pneumatic operation conditions of MIHA

Technical Field

The invention belongs to the field of reactor and modeling technology, and particularly relates to a modeling method of a phase interface area regulation model under MIHA pure pneumatic operation conditions.

Background Art

Out of consideration for global environmental protection, marine fuel oil must reduce the sulfur content. For example, the sulfur content of marine fuel oil on the high seas must be reduced to 0.5%. Therefore, it is imperative to replace high-sulfur residual fuel oil with low-sulfur distillate fuel oil. Most of the sulfur in crude oil exists in residual oil. The sulfur in residual oil is mainly distributed in aromatics, colloids and asphaltene, of which most of the sulfur exists in the form of five-membered ring thiophene and thiophene derivatives. Generally, the C-S bond of the residual oil macromolecule is broken by hydrogenolysis reaction to convert sulfur into hydrogen sulfide to remove sulfur from the residual oil. The sulfur present in non-asphaltene is easier to remove under hydrogenation conditions and can achieve a higher conversion depth. However, since asphaltene is the macromolecule with the largest relative molecular mass, the most complex structure and the strongest polarity in the residual oil, the sulfur in it is difficult to remove, resulting in a limited desulfurization rate during the residual oil hydrodesulfurization process.

In the process of residual oil hydrodesulfurization reaction (hereinafter referred to as MIHA), the conversion of sulfur-containing asphaltene is of vital importance. The core part of asphaltene is a highly condensed fused aromatic ring system. The fused aromatic ring system is surrounded by alkyl and cycloalkyl structures of varying numbers and sizes. It is the component with the highest degree of condensation in residual oil. It also contains heteroatoms such as S, N, O, and metals, and has a complex morphology and molecular structure. In the process of residual oil hydroconversion, asphaltene mainly undergoes two types of reactions in opposite directions: cracking from macromolecules to small molecules and condensation of small molecules to generate macromolecules through dehydrogenation polymerization. The present invention uses the asphaltene hydrodesulfurization reaction as a model reaction of the residual oil hydrogenation process to investigate the effects of reactor structure, system physical properties, operating parameters, and input energy on the interfacial area in the bubble breaker.

Summary of the invention

The purpose of the present invention is to provide a modeling method for the interfacial area control model under MIHA pure pneumatic operating conditions, so as to study the influence of reactor structure, system physical properties and operating parameters, and input energy on the interfacial area, thereby providing guidance for the design of MIHA reactors and the design of MIHA reaction systems.

MIHA microbubbles can be formed in three ways, namely: pure liquid, pure pneumatic and gas-liquid linkage. Under pure liquid and pure pneumatic operation conditions, the energy required for system operation and microbubble formation is completely provided by liquid mechanical energy or gas static pressure energy; under gas-liquid linkage operation conditions, gas static pressure energy and liquid mechanical energy simultaneously provide the energy required for system operation and microbubble formation. The present invention explores the modeling method of the bubble scale control model under pure pneumatic operation conditions. According to the above research, the phase interface area is related to the gas content and the Sauter average diameter _d32 of the microbubbles. Based on this, the method of the present invention includes the following steps:

S100. Analyze the bubble generation process under pure pneumatic conditions and establish an energy conversion model in the bubble breaker;

Under pure pneumatic operation conditions, the liquid flow rate Q _L << gas flow rate Q _G , before the gas is introduced, the bubble breaker is filled with static reaction liquid; it is assumed that the system liquid is in a closed loop, that is, the amount of liquid does not change during the whole process; due to the entry of gas, part of the liquid will be forced to enter the outer circulation pipeline of the bubble breaker; the bubble breaker length is set to L, the diameter is D ₁ , and the cross-sectional area is S ₁ ＝πD ₁ ² /4; the nozzle diameter is D _N ;

The following assumptions are made:

(1) Steady-state operation, the operating pressure _Pm is constant;

(2) Since the actual operating pressure is relatively high, the change in liquid potential energy and the change in gas pressure inside the bubble caused by the bubble interfacial tension are ignored;

(3) Since the density of gas is much smaller than that of liquid, the kinetic energy of the input gas is ignored;

Taking the bubble breaker as the control body, the energy balance under steady-state conditions is carried out. Under pneumatic conditions, when the gas with pressure P _G0 and volume flow rate Q _G0 enters the bubble breaker with constant operating pressure P _m , the gas releases part of the static pressure energy, which is converted into liquid kinetic energy and bubble surface energy. The static pressure energy released by the gas is equivalent to the work W _G done by the gas on the system. According to the definition of work, it can be known that:

Q _G is the gas flow rate in the bubble breaker. Assuming that the gas is an ideal gas, the ideal gas state equation can be obtained:

In formula (2), ρ _G0 and _MA are the gas density and gas molar mass entering the crusher, respectively; R and T are the gas constant and gas temperature, respectively;

Substituting formula (2) into formula (1) and integrating, we can obtain:

Let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be ΔP, that is:

ΔP＝P _G0 -P _m (32)

Since ΔP>0, _WG <0, that is, the mechanical energy of the gas will decrease after entering the bubble breaker. Since the operating pressure _Pm of the bubble breaker is constant and the gravitational potential energy of the liquid is relatively negligible, the reduced mechanical energy of the gas will be converted into liquid kinetic energy and bubble interface energy. Therefore, the following relationship can be obtained from equations (3) and (4):

The left side of equation (5) is the decrease in gas static pressure energy, i.e. _-WG ; the two terms on the right side of equation (5) are the liquid kinetic energy and the gas-liquid interface energy, respectively; where _ρL and _σL are the liquid density and the interface tension, respectively; _UL is the linear velocity of the liquid flowing out of the breaker; _d32 is the Sauter mean diameter of the bubbles flowing out of the bubble breaker; based on mass balance, _QG and _QG0 have the following relationship:

Since ΔP＜＜P _m , Q _G ≈Q _G0 ; preliminary calculations show that the gas-liquid interface energy value can be ignored relative to the liquid kinetic energy value, so equation (5) can be simplified to:

S200. Calculate the liquid flow rate based on the energy conversion model and liquid circulation within the bubble breaker;

Since the liquid in and out of the crusher is a closed-loop cycle, that is, the in and out liquid flow rates are equal, we have:

Q _L ＝U _L S ₁ (1-φ _G ) (36)

The gas content _φG in the bubble breaker is calculated as follows:

From (8) and (9), we can get:

_UL is the superficial velocity of the gas-liquid mixture in the bubble breaker. Substituting equation (10) into equation (7), we can obtain:

The liquid flow rate Q _L at the nozzle diameter caused by the gas input can be calculated by equation (11), and equation (7) can be obtained:

Under pure pneumatic operating conditions, Q _L << Q _G , equation (11) is simplified to:

From this we get:

From the ideal state equation, we can see that there is the following relationship:

Substituting equation (15) into equation (14), we can obtain:

From equation (16), we can see that the bubble breaker cross-sectional area _S1 has a greater influence on the liquid circulation flow rate _QL ;

because:

Where V _N is the flow velocity at the nozzle;

When V _N is constant, we can get from equations (16) and (17):

When D _N is constant, we can get from equations (16) and (17):

From equations (10) and (16), we can get:

This completes the estimation of Q _L under purely aerodynamic conditions;

S300. Calculate the energy dissipation rate ε _mix in the gas-liquid intense mixing zone;

According to the first law of thermodynamics:

In the above formula, _Lmix is the length of the intense gas-liquid mixing zone in the bubble crusher, m; _λ1 is the ratio of the gas-liquid volume flow rate, _λ1 = _QG / _QL ; _K1 is the ratio of the bubble crusher nozzle diameter to the crusher diameter, _K1 = _DN / _D1 ;

_Lmix is related to the length of the maximum liquid velocity in the bubble breakup zone that decays until it disappears. During the decay process of the maximum liquid velocity, the decay law of its centerline velocity _Ujm is not affected by the surrounding bubble disturbance and conforms to the following decay law:

In equation (22), x is the horizontal distance from the core of the bubble breaker to the maximum velocity. When U _jm decays to the apparent velocity of the gas-liquid mixture _UL , the high speed disappears, and then a uniform gas-liquid mixture flow is formed; therefore, L _mix is the x value when U _jm = _UL , that is:

After simplifying equation (23), we can get:

Substituting equation (24) into equation (21) and simplifying it, we can obtain:

By combining equations (16), (20) and equation (25), ε _mix can be calculated.

S400. Calculate the bubble size of microbubbles in MIHA;

The microbubbles d ₃₂ in MIHA can be calculated based on the inventors’ previous studies;

d _max ＝0.75(σ _L /ρ _L ) ^0.6 ε _mix ^-0.4 (54)

d _min =11.4(μ _L /ρ _L ) ^0.75 ε _mix ^-0.25 (55)

Wherein, d _min is the minimum diameter of the bubble; d _max is the maximum diameter of the bubble; μ _L is the dynamic viscosity of the liquid;

S500. Calculate the interfacial area of micro gas-liquid system;

The interfacial area is calculated according to the following formula:

Another object of the present invention is to provide a phase interface area control model under pure pneumatic operating conditions of MIHA constructed by the above method.

Another object of the present invention is to provide a reactor designed by the above method.

The reactor structure of the present invention can be found in the patent CN106187660A previously applied by the inventor, which will not be described in detail in the present invention. The present invention utilizes the constructed model reactor structure, system physical properties and operating parameters, and the influence of input energy on bubble size, so that relevant reactor structure parameters can be designed according to needs.

The method of the present invention establishes a phase interfacial area control model under pure pneumatic operating conditions for MIHA, which comprehensively reflects the influence of reactor structure, system physical properties, operating parameters, and input energy on the phase interfacial area, and can provide guidance for reactor design and MIHA reaction system design, and guide the design of efficient reactor structure and reaction system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of the physical model of bubble generation process under pure pneumatic conditions;

Figure 2 shows the effect of operating pressure on the phase interface area a;

FIG3 is the effect of operating temperature on the phase interface area a;

Figure 4 shows the effect of the air supply pressure difference ΔP on the phase interface area a;

Figure 5 shows the effect of ventilation volume Q _G on the phase interface area a.

DETAILED DESCRIPTION

The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.

Example 1

S100. Analyze the bubble generation process under pure pneumatic conditions and establish an energy conversion model in the bubble breaker;

Before the gas is introduced, the bubble breaker is filled with static reaction liquid. When the gas is introduced, due to the pressure difference ΔP between the gas pressure _PG and the system operating pressure _Pm , the gas static pressure energy will be transferred to the liquid, causing the liquid to turbulent, and the gas pressure itself will quickly drop to the operating pressure in the MIHA. Due to the flow of gas and liquid, the gas and liquid flow out of the bubble breaker. For pneumatic operating conditions, the liquid flow rate _QL is much smaller than the gas flow rate _QG , and the energy required for system operation is almost entirely provided by the gas pressure energy.

Establish a physical model diagram as shown in Figure 1:

Assume that the system liquid is in a closed loop, that is, the amount of liquid does not change during the whole process. Due to the entry of gas, part of the liquid will be forced into the outer circulation pipeline of the bubble breaker. The length of the bubble breaker is set to L (m), the diameter is D ₁ (m), and the cross-sectional area is S ₁ (m ² ) (S ₁ ＝πD ₁ ² /4). The nozzle diameter is D _N (m).

The following assumptions are made:

(1) Steady-state operation, the operating pressure _Pm is constant;

(2) Since the actual operating pressure is relatively high, the change in liquid potential energy and the change in gas pressure inside the bubble caused by the bubble interfacial tension are ignored;

(3) Since the density of gas is much smaller than that of liquid, the kinetic energy of the input gas is neglected.

The bubble breaker is used as the control body to perform energy balance under steady-state conditions. Under pneumatic conditions, when a gas with a pressure of P _G0 (Pa) and a volume flow rate of Q _G0 (m ³ /s) enters a bubble breaker with a constant operating pressure of P _m (Pa), the gas releases part of its static pressure energy, which is converted into liquid kinetic energy and bubble surface energy. The static pressure energy released by the gas is equivalent to the work W _G (W) done by the gas on the system. According to the definition of work, it can be seen that:

Q _G (m ³ /s) is the gas flow rate in the bubble breaker. For the sake of simplicity, it is assumed that the gas is an ideal gas within the scope of the present invention. According to the ideal gas state equation, it can be obtained that:

In formula (2), ρ _G0 (Kg/m ³ ) and _MA (Kg/mol) are the density and molar mass of the gas entering the crusher, respectively; R (8.314 J/mol.K) and T (K) are the gas constant and gas temperature, respectively.

Substituting formula (2) into formula (1) and integrating, we can obtain:

Let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be ΔP (Pa), that is:

ΔP＝P _G0 -P _m (60)

Since ΔP>0, _WG <0, that is, the mechanical energy of the gas will decrease after entering the bubble breaker. Since the operating pressure _Pm of the bubble breaker is constant and the gravitational potential energy of the liquid is relatively negligible, the reduced mechanical energy of the gas will be converted into the kinetic energy of the liquid and the bubble interface energy. Therefore, the following relationship can be obtained from equations (3) and (4):

The left side of equation (5) is the decrease in gas static pressure energy (-W _G ), which is also the energy source required for the operation of the system; the two terms on the right side of equation (5) are the liquid kinetic energy and the gas-liquid interface energy, respectively. Among them, ρ _L (Kg/m ³ ) and σ _L (N/m) are the liquid density and interfacial tension, respectively; U _L (m/s) is the linear velocity of the liquid flowing out of the breaker; d ₃₂ (m) is the Sauter average diameter of the bubbles flowing out of the bubble breaker; based on mass balance, Q _G and Q _G0 have the following relationship:

For the present invention, ΔP＜＜P _m , therefore, Q _G ≈Q _G0 . For the convenience of description, the inlet and outlet gas flow rates are all represented by Q _G. Preliminary calculations show that the gas-liquid interface energy value can be ignored relative to the liquid kinetic energy value. This article first ignores this term and then verifies it through calculation. Therefore, equation (5) can be simplified to:

S200. Calculate the liquid flow rate based on the energy conversion model and liquid circulation within the bubble breaker;

According to the closed-loop assumption in the previous article, the inlet and outlet liquid flows are equal, so we have

Q _L ＝U _L S ₁ (1-φ _G ) (64)

Among them, the gas content φ _G in the bubble breaker can be calculated as follows:

From (8) and (9), we can get:

Obviously, _UL is the superficial velocity of the gas-liquid mixture in the bubble breaker. Substituting equation (10) into equation (7) yields:

Equation (11) can be used to calculate the liquid flow rate Q _L at the nozzle diameter caused by gas input, but the form is relatively complicated and must be reasonably simplified according to the actual situation of this project. Equation (7) can be obtained:

Calculations show that, under the conditions studied in the present invention, Q _L << Q _G . Therefore, equation (11) can be simplified to:

From this we get:

In fact, from the ideal state equation, we know that there is the following relationship:

Substituting equation (15) into equation (14), we can obtain:

From equation (16), we can see that the bubble breaker cross-sectional area _S1 has a greater influence on the liquid circulation flow rate _QL ;

because:

Where V _N is the flow velocity at the nozzle;

When V _N is constant, we can get from equations (16) and (17):

When D _N is constant, we can get from equations (16) and (17):

From equations (10) and (16), we can get:

The above is based on a rough calculation of Q _L under full aerodynamic conditions. Then the diameter D _N is determined based on the known V _N (when D _N is constant, V _N can also be calculated).

S300. Calculate the energy dissipation rate ε _mix in the gas-liquid intense mixing zone;

d ₃₂ is closely related to the energy dissipation rate ε _mix in the gas-liquid intense mixing zone in the bubble breaker. According to the first law of thermodynamics, it can be obtained that:

In the above formula, _Lmix is the length of the intense gas-liquid mixing zone in the bubble crusher, m; _λ1 is the ratio of the gas-liquid volume flow rate ( _λ1 = _QG / _QL ). _K1 is the ratio of the bubble crusher nozzle diameter to the crusher diameter ( _K1 = _DN / _D1 ).

Evans et al. have derived a mathematical model of L _mix based on the principle of conservation of kinetic energy, but it is not applicable to the situation involved in the present invention, so it needs to be re-derived. The present invention believes that L _mix is related to the length of the maximum flow rate of the liquid in the bubble breakup zone until it disappears. During the attenuation of the maximum flow rate of the liquid, the attenuation law of its centerline velocity U _jm is not affected by the surrounding bubble disturbance and conforms to the following attenuation law:

In equation (22), x is the horizontal distance from the core of the bubble breaker to the maximum velocity. When U _jm decays to the superficial velocity of the gas-liquid mixture _UL , the high speed disappears, and then a uniform gas-liquid mixture flow is formed. Therefore, L _mix is the x value when U _jm = _UL .

Right now:

After simplifying equation (23), we can get:

Substituting equation (24) into equation (21) and simplifying it, we can obtain:

By combining equations (16), (20) and equation (25), ε _mix can be calculated.

S400. Calculate the bubble size of microbubbles in MIHA;

The microbubble d ₃₂ in MIHA is calculated according to the following formula:

d _max =0.75(σ _L /ρ _L ) ^0.6 ε _mix ^-0.4 (82)

d _min =11.4(μ _L /ρ _L ) ^0.75 ε _mix ^-0.25 (83)

Wherein, d _min is the minimum diameter of the bubble; d _max is the maximum diameter of the bubble; μ _L is the dynamic viscosity of the liquid;

S500. Calculate the interfacial area of micro gas-liquid system;

The interfacial area is calculated according to the following formula:

Example 2

This example specifically illustrates the phase interface area control model constructed based on the method of Example 1.

The phase interface area control model obtained based on the modeling method of Example 1 is as follows:

d _max ＝0.75(σ _L /ρ _L ) ^0.6 ε _mix ^-0.4 (89)

d _min =11.4(μ _L /ρ _L ) ^0.75 ε _mix ^-0.25 (90)

Example 3

This example is based on the modeling method of Example 1, and studies the effects of operating pressure, operating temperature, gas supply pressure difference ΔP and ventilation volume _QG on the phase interface area for a specific reactor structure and reaction system.

The general calculation conditions are as follows:

The diameter of the breaker is D ₁ = 0.02 m; the ratio of the diameter of the bubble breaker nozzle to the diameter of the breaker is K ₁ = 0.5;

Residue oil density ρ _L = 800Kg/m ³ ;

The fitting formula of residual oil interfacial tension σ _L is as follows:

σ _L =[31.74-0.04775(T+273.15)]×10 ^-3 (N/m);

The fitting formula of residual oil dynamic viscosity μ _L is as follows;

(1) Effect of operating pressure on the interfacial area a;

The calculation conditions are as follows:

Ventilation volume Q _G = 80 L/h; operating pressure P _m = 10-20 MPa; gas supply pressure difference ΔP = 6 MPa; gas temperature T = 500°C.

As shown in Figure 2, it can be seen that the operating pressure P _m has little effect on the gas-liquid interface area a. The main reason is that P _m has little effect on the liquid circulation flow Q _L. Analyzing the effect of P _m on Q _L reflected in the above equation (16), it can be seen that;

项是减小的，最终Q_L受P_m的影响极小。此外，Q_L是决定d₃₂以及气含率φ_G的关键因素，而后两者通过方程(29)决定a的大小。因此，操作压力P_m对a的上述影响是合理的。When P _m increases, the term (P _m +ΔP) increases, and

The term is reduced, and finally Q _L is minimally affected by P _m . In addition, Q _L is the key factor in determining d ₃₂ and gas holdup φ _G , and the latter two determine the size of a through equation (29). Therefore, the above influence of operating pressure P _m on a is reasonable.

(2) The effect of operating temperature on the interfacial area a;

The calculation conditions are as follows:

Ventilation volume Q _G = 80 L/h; operating pressure P _m = 14 MPa; gas supply pressure difference ΔP = 6 MPa; gas temperature T = 400-500°C.

The effect of operating temperature on a is shown in Figure 3. It can be seen that the gas-liquid interface area a increases with the increase of operating temperature. The main reason is that when the operating temperature of the system is changed alone, the gas-liquid interface area a is only affected by d ₃₂ .

(3) The effect of the air supply pressure difference ΔP on the phase interface area a;

The calculation conditions are as follows:

Residue oil density ρ _L =800 Kg/m ³ ; operating pressure P _m =14 MPa; gas supply pressure difference ΔP=1-10 MPa; gas temperature T=450°C.

The results are shown in Figure 4 (air flow rate 80L/h); it can be seen that as the air supply pressure difference increases, the energy dissipation rate of the bubble breaker increases, and the gas-liquid interface area decreases. When the energy dissipation rate of the bubble breaker increases, the bubble diameter decreases. Since it is a fully pneumatic method, the increase in the air supply pressure difference will inevitably accelerate the flow of the liquid in the reactor, which produces two results: on the one hand, the turbulence of the liquid in the bubble breaker increases, resulting in an increase in the energy dissipation rate and a decrease in bubbles; on the other hand, the residence time of the bubbles in the reactor is shortened, resulting in a decrease in the gas holdup, and the latter effect is more obvious, which will result in a decrease in the gas-liquid interface area.

(4) The effect of ventilation volume Q _G on the phase interface area a;

The calculation conditions are as follows:

Ventilation volume Q _G = 1 ~ 100L/h; operating pressure P _m = 14MPa; gas supply pressure difference ΔP = 0.1 ~ 10MPa; gas temperature T = 500°C.

The results are shown in FIG5 ; it can be seen that the gas-liquid interface area a in the reactor increases with the increase of the ventilation rate, which is approximately a linear relationship.

Claims (2)

1. a phase boundary area control model modeling method under a MIHA pure aerodynamic operation condition, is characterized in that, comprises the steps: S100. Analyze the bubble generation process under pure aerodynamic conditions, and establish an energy conversion model in the bubble breaker; Under purely pneumatic operating conditions, the liquid flow rate Q _L << gas flow rate Q _G , before the gas is introduced, the bubble breaker is filled with static reaction liquid; the liquid in the system is a closed circuit, that is, the liquid volume does not change during the whole process; The entry of gas will cause part of the liquid to be forced into the external circulation pipeline of the bubble breaker; set the length of the bubble breaker as L, the diameter as D ₁ , the cross-sectional area S ₁ = πD ₁ ² /4; the diameter of the nozzle as D _N ; The calculation premise is as follows: (1) Steady-state operation, the operating pressure P _m is constant; (2) Due to the high actual operating pressure, the change of liquid potential energy and the change of gas pressure in the bubble caused by the interfacial tension of the bubble are ignored; (3) Since the density of gas is much smaller than that of liquid, the kinetic energy of the input gas is ignored; Taking the bubble breaker as the control body, the energy balance calculation under steady-state conditions is carried out; under aerodynamic conditions, when the gas with the pressure P _G0 and the volume flow rate Q _G0 enters the bubble breaker with a constant operating pressure P _m , the gas releases Part of the static pressure energy is converted into liquid kinetic energy and bubble surface energy; the static pressure energy released by the gas is equivalent to the work W _G performed by the gas on the system, according to the definition of work:

Q _G is the gas flow rate in the bubble breaker, according to the ideal gas state equation:

In formula (2), ρ _G0 and _MA are the gas density and gas molar mass entering the crusher, respectively; R and T are the gas constant and gas temperature, respectively; Substitute formula (2) into formula (1) and integrate to get:

Let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be ΔP, namely: ΔP＝P _G0 -P _m (4) Since ΔP>0, _WG <0, that is, the mechanical energy of the gas will decrease after entering the bubble breaker; since the operating pressure P _m of the bubble breaker is constant, and the gravitational potential energy of the liquid is ignored, the reduced mechanical energy of the gas will be converted into Liquid kinetic energy and bubble interface energy; therefore, from formula (3) (4):

The left side of the equal sign in equation (5) is the reduction of gas static pressure energy, i.e. -W _G ; the two items on the right side of the equal sign in equation (5) are liquid kinetic energy and gas-liquid interface energy respectively; among them, ρ _L and σ _L are liquid density respectively and interfacial tension; U _L is the linear velocity of the liquid flowing out from the breaker; d ₃₂ is the average Sauter diameter of the bubbles flowing out from the bubble breaker; according to mass balance, Q _G and Q _G0 have the following relationship:

Since ΔP<<P _m , so Q _G ≈Q _G0 ; ignoring the gas-liquid interfacial energy value relative to the liquid kinetic energy value, the equation (5) is simplified as:

S200. Calculate the liquid flow rate based on the energy conversion model and liquid circulation in the bubble breaker; Since the liquid entering and exiting the crusher is a closed circuit, that is, the flow of liquid entering and exiting is equal, so there are: Q _L ＝ U _L S ₁ (1-φ _G ) (8) Among them, the gas holdup φ _G in the bubble breaker is calculated by the following formula:

From (8) (9) can get:

U _L is the superficial velocity of the gas-liquid mixture in the bubble breaker, which can be obtained by substituting equation (10) into equation (7):

The liquid flow Q _L at the diameter of the nozzle due to gas input can be calculated from equation (11), and from equation (7):

Under purely pneumatic operating conditions, Q _L << Q _G , then equation (11) can be simplified as:

From this we get:

According to the ideal state equation, there is the following relationship:

Substituting equation (15) into equation (14), we can get:

From equation (16), it can be seen that the cross-sectional area S ₁ of the bubble breaker has a greater influence on the liquid circulation flow rate Q _L ; because:

Where V _N is the flow velocity at the nozzle; When V _N is constant, it can be obtained from equations (16) and (17):

When D _N is constant, it can be obtained from formulas (16) and (17):

From equations (10) and (16), we can get:

In this way, the estimation of Q _L under pure aerodynamic conditions is completed; S300. Calculate the energy dissipation rate ε _mix in the strong gas-liquid mixing zone; According to the first law of thermodynamics:

In the above formula, L _mix is the length of the gas-liquid intense mixing zone in the bubble breaker, m; λ ₁ is the ratio of gas-liquid volume flow rate, λ ₁ =Q _G /Q _L ; K ₁ is the diameter of the nozzle of the bubble breaker and the diameter of the breaker The ratio of K ₁ =D _N /D ₁ ; L _mix is related to the length at which the highest liquid velocity decays until it disappears in the bubble crushing zone. During the decay process of the maximum liquid velocity, the decay law of its centerline velocity U _jm is not affected by the disturbance of the bubbles around it, and conforms to the following decay law :

In equation (22), x is the horizontal distance from the core of the bubble breaker to the maximum velocity; when U _jm decays to the superficial velocity U _L of the gas-liquid mixture, the high speed disappears, and then a uniform gas-liquid mixture flow will be formed; therefore, L _mix is the x value when U _jm = U _L , namely:

After simplifying equation (23), we can get:

After substituting equation (24) into (21) and simplifying, we get:

ε _mix can be calculated by combining equations (16)(20) and equation (25); S400. Calculate the bubble size of the microbubbles in the MIHA; The microbubble d ₃₂ in MIHA is calculated according to the following formula; d _max ＝0.75(σ _L /ρ _L ) ^0.6 ε _mix ^-0.4 (26) d _min ＝11.4(μ _L /ρ _L ) ^0.75 ε _mix ^-0.25 (27)

Among them, d _min is the minimum diameter of the bubble; d _max is the maximum diameter of the bubble; μ _L is the dynamic viscosity of the liquid; S500. Calculate the phase boundary area of the micro-gas-liquid system; The phase boundary area is calculated according to the following formula:

2. The reactor designed by the method according to claim 1.

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