CN109657406B - Modeling method of phase boundary area regulation model under MIHA pure pneumatic operation condition - Google Patents
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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
Technical Field
The invention belongs to the technical field of reactors and modeling, and particularly relates to a modeling method of a phase boundary area regulation model under an MIHA pure pneumatic operation condition.
Background
For global environmental protection, the sulfur content of the marine fuel oil must be reduced, for example, the sulfur content of the open sea marine fuel oil must be reduced to 0.5%, so that it is imperative to replace the high sulfur residue fuel oil with the low sulfur distillate fuel oil. Most of the sulfur in crude oil is present in residuum, which is mainly distributed in aromatics, colloids and asphaltenes, with most of the sulfur being present in the form of five membered ring thiophenes and thiophene derivatives. The sulfur in the residuum is typically removed by breaking the C-S bonds of the residuum macromolecules via a hydrogenolysis reaction to convert the sulfur to hydrogen sulfide. Sulfur present in non-asphaltenes is easier to remove under hydrogenation conditions and can reach higher conversion depths. However, asphaltene is a macromolecule with the largest relative molecular mass, the most complex structure and the strongest polarity in the residual oil, so that sulfur in the macromolecule is difficult to remove, and the desulfurization rate in the residual oil hydrodesulfurization process is limited.
The conversion of sulfur-containing asphaltenes is critical during residuum hydrodesulfurization (hereinafter MIHA). The core of asphaltenes is a highly condensed, fused aromatic ring system. The condensed aromatic ring system is provided with alkyl and cycloalkyl structures with different numbers and sizes, is the component with the largest condensation degree in residual oil, contains heteroatoms such as S, N, O, metal and the like, and has complex morphology and molecular structure. In the residuum hydroconversion process, asphaltene mainly undergoes two reactions of cracking from macromolecules to small molecules and condensation from small molecule dehydrogenation polymerization to macromolecules. The invention takes asphaltene hydrodesulfurization reaction as a model reaction of residual oil hydrogenation process, and examines the influence of the structure, physical properties of a system, operation parameters and input energy of a reactor on the inner phase boundary area of a bubble breaker.
Disclosure of Invention
The invention aims to provide a modeling method of a phase boundary area regulation model under the MIHA pure pneumatic operation condition so as to study the influence of the structure, system physical properties, operation parameters and input energy on the phase boundary area, thereby realizing the guidance on the MIHA reactor design and the MIHA reaction system design.
MIHA microbubbles can be formed in three ways: pure hydraulic, pure pneumatic and gas-liquid linkage. Under the pure hydraulic and pure pneumatic operation conditions, the energy required by the system operation and the formation of micro bubbles is completely provided by liquid mechanical energy or gas static pressure energy; under the condition of gas-liquid linkage operation, the gas static pressure energy and the liquid mechanical energy simultaneously provide the energy required by system operation and micro-bubble formation. The invention discusses a modeling method of a bubble scale regulation model under the pure pneumatic operation condition, and according to the previous research, the phase boundary area and the gas content and the average diameter d of the micro bubbles Sauter 32 In relation thereto, the method of the invention comprises the steps of:
s100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
under purely pneumatic operating conditions, the liquid flow rate Q L <<Gas flow rate Q G Before the gas is not introduced, the bubble breaker is filled with static reaction liquid; assuming that the system liquid is in closed cycle, namely the liquid amount does not change in the whole process; part of the liquid is forced to enter the outer circulation pipeline of the bubble breaker due to the entering of the gas; setting the length of the bubble breaker as L and the diameter as D 1 Cross-sectional area S 1 ＝πD 1 2 4; nozzle diameter D N ；
The assumptions are made as follows:
(1) Steady state operation, operating pressure P m Constant;
(2) The change of potential energy of liquid and the change of gas pressure in the bubbles caused by interfacial tension of the bubbles are ignored because of higher actual operation pressure;
(3) Since the gas density is much smaller than the liquid, the kinetic energy of the input gas is ignored;
taking a bubble breaker as a control body, and performing energy balance under a steady-state condition; under pneumatic conditions, the pressure is P G0 The volume flow is Q G0 Is constant at P m When the bubble breaker is used, part of static pressure energy is released by the gas and is converted into liquid kinetic energy and bubble surface energy; the static pressure energy released by the gas is equivalent to the work W of the gas on the system G According to the work definition, it can be seen that:
Q G for the gas flow in the bubble breaker, assuming that the gas is ideal gas, it is obtained according to the ideal gas state equation:
in the formula (2), ρ G0 And M A (the density and molar mass of the gas entering the breaker; R and T are the gas constant and the gas temperature, respectively;
substituting formula (2) into formula (1) and integrating to obtain:
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 (32)
since ΔP > 0, W is G < 0, i.e. the mechanical energy of the gas will be reduced after it enters the bubble breaker; due to bubble breaker operating pressure P m Constant and relatively negligible liquid gravitational potential energy, so the reduced mechanical energy of the gas will be converted into liquid kinetic energy and bubble interface energy; the following relationship can be obtained from the formulas (3) and (4):
the left side of the equal sign of equation (5) is the reduction of the static pressure energy of the gas, namely-W G The method comprises the steps of carrying out a first treatment on the surface of the The right two terms of the equal sign of the equation (5) are respectively liquid kinetic energy and gas-liquid interface energy; wherein ρ is L Sum sigma L Liquid density and interfacial tension, respectively; u (U) L Is the linear velocity of the liquid flowing out of the disrupter; d, d 32 An average diameter of the air bubbles Sauter flowing out from the air bubble breaker; q is calculated according to mass balance G And Q is equal to G0 The following relationship is provided:
due to DeltaP < P m Thus Q G ≈Q G0 The method comprises the steps of carrying out a first treatment on the surface of the Preliminary calculations indicate that the gas-liquid interface energy value is negligible relative to the liquid kinetic energy value, and therefore equation (5) can be simplified as:
s200, calculating liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
since the liquid entering and exiting the crusher is in closed cycle, i.e. the flow rates of the liquid entering and exiting are equal, the liquid entering and exiting are:
Q L ＝U L S 1 (1-φ G ) (36)
wherein the gas content in the bubble breaker phi G Calculated as follows:
from formulas (8) (9):
U L substituting equation (7) for the apparent velocity of the gas-liquid mixture in the bubble breaker, it is possible to obtain:
from equation (11), the liquid flow rate Q at the nozzle diameter due to the gas input can be calculated L From equation (7):
under purely pneumatic operating conditions, Q L <<Q G Then equation (11) is reduced to:
this gives:
from the ideal state equation, the following relationship exists:
substituting equation (15) into equation (14) yields:
from equation (16), it can be seen that: bubble breaker cross-sectional area S 1 For liquid circulation flow rate Q L The effect is greater;
as a result of:
v in N Is the flow rate at the nozzle;
when V is N At a certain time, it is obtainable by formulas (16) and (17):
when D is N At a certain time, it is obtainable by formulas (16) and (17):
from formulae (10) and (16):
thereby completing the Q under the pure pneumatic condition L Is determined by the estimation of (a);
s300, calculating energy dissipation rate epsilon of gas-liquid intensive mixing area mix ；
According to the first law of thermodynamics:
in the above, L mix The length of a gas-liquid intensive mixing zone in bubble breaking is m; lambda (lambda) 1 Lambda is the ratio of the gas to the liquid volume flow 1 ＝Q G /Q L ；K 1 K is the ratio of the diameter of the bubble breaker nozzle to the diameter of the breaker 1 ＝D N /D 1 ；
L mix In connection with the length of the decay of the liquid maximum flow velocity in the bubble breaking zone until it has disappeared, the liquid maximum flow velocity during its decay, the central line velocity U jm The attenuation law of (2) is not influenced by the disturbance of surrounding bubbles, and accords with the following attenuation law:
in equation (22), x is the horizontal distance from the bubble breaker core to the maximum speed. When U is jm Decaying to the apparent speed U of the gas-liquid mixture L At this time, the high velocity disappears, after which a uniform gas-liquid mixture stream will be formed; thus, L mix Is U (U) jm ＝U L The value of x at that time, namely:
the equation (23) can be simplified to obtain:
substituting equation (24) into (21) and simplifying to obtain:
combining (16) (20) and equation (25) to calculate ε mix 。
S400, calculating the bubble size of micro bubbles in the MIHA;
microbubbles d in MIHA 32 Calculation may be performed based on prior studies by the inventors;
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, d max Is the maximum diameter of the bubble; mu (mu) L Is hydrodynamic viscosity;
s500, calculating the phase boundary area of the micro gas-liquid system;
the phase boundary area is calculated according to the following formula:
another object of the present invention is to provide a phase boundary area control model under the pure pneumatic operating condition of MIHA constructed by the above method.
It is a further object of the present invention to provide a reactor designed by the above process.
The structure of the reactor of the present invention can be seen in the patent CN106187660a previously filed by the inventor, and the description of the present invention is omitted. The invention utilizes the influence of constructed model reactor structure, system physical property and operation parameter and input energy on bubble scale, thereby carrying out relevant reactor structure parameter design according to the requirement.
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.
Drawings
FIG. 1 is a schematic diagram of a physical model of a bubble generation process under purely pneumatic conditions;
FIG. 2 is the effect of operating pressure on phase boundary area a;
FIG. 3 is the effect of operating temperature on phase boundary area a;
fig. 4 is the effect of the air supply pressure difference Δp on the phase boundary area a;
FIG. 5 is ventilation Q G Impact on phase boundary area a.
Detailed Description
The technical scheme of the invention is further described below with reference to the attached drawings and the detailed description.
Example 1
S100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
before the gas is not introduced, the bubble breaker is filled with a static reaction liquid. After the start of the gas introduction, due to the gas pressure P G And system operating pressure P m There is a pressure difference deltap between them, the hydrostatic energy of the gas will be transferred to the liquid, causing turbulence of the liquid, and the pressure of the gas itself will drop rapidly to the operating pressure within the MIHA. Due to the flow of the gas-liquid two phases, the gas-liquid flows out from the bubble breaker. For pneumatic operating conditions, the liquid flow rate Q L Much smaller than the gas flow Q G The energy required for the system to operate is almost entirely provided by the gas pressure energy.
Establishing a physical model diagram as shown in fig. 1:
the system liquid is assumed to be in closed cycle, i.e. the liquid amount does not change in the whole process. Part of the liquid will be forced into the bubble breaker external circulation line due to the ingress of gas. Setting the length of the bubble breaker to L (m)Diameter D 1 (m) cross-sectional area S 1 (m 2 )(S 1 ＝πD 1 2 /4). Nozzle diameter D N (m)。
The assumptions are made as follows:
(1) Steady state operation, operating pressure P m Constant;
(2) The change of potential energy of liquid and the change of gas pressure in the bubbles caused by interfacial tension of the bubbles are ignored because of higher actual operation pressure;
(3) Since the gas density is much smaller than the liquid, the kinetic energy of the input gas is ignored.
The energy balance under steady state conditions was performed using a bubble breaker as a control body. Under pneumatic conditions, the pressure is P G0 (Pa) and a volume flow of Q G0 (m 3 Gas inlet operating pressure of/s) is constant at P m The bubble breaker of (Pa) converts partial static pressure energy of gas released into liquid kinetic energy and bubble surface energy. The static pressure energy released by the gas is equivalent to the work W of the gas on the system G (W) according to the work definition:
Q G (m 3 s) is the gas flow rate in the bubble breaker, and for simplicity, it is assumed that the gas is an ideal gas within the scope of the present invention, and is obtained according to the ideal gas state equation:
in the formula (2), ρ G0 (Kg/m 3 ) And M A (Kg/mol) is the density and molar mass of the gas entering the breaker, respectively; r (8.314J/mol.K) and T (K) are the gas constant and the gas temperature, respectively.
Substituting formula (2) into formula (1) and integrating to obtain:
let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be Δp (Pa), namely:
ΔP＝P G0 -P m (60)
since ΔP > 0, W is G < 0, i.e. the mechanical energy of the gas will be reduced after it enters the bubble breaker. Due to bubble breaker operating pressure P m Constant and relatively negligible liquid gravitational potential energy, so the reduced mechanical energy of the gas will be converted into liquid kinetic energy and bubble interface energy. The following relationship can be obtained from the formulas (3) and (4):
to the left of equation (5) is a reduction in gas static pressure energy (-W) G ) Namely, the energy source required by the system operation is adopted; the right two terms of the equation (5) are respectively the liquid kinetic energy and the gas-liquid interface energy. Wherein ρ is L (Kg/m 3 ) Sum sigma L (N/m) liquid density and interfacial tension, respectively; u (U) L (m/s) the linear velocity of the liquid flowing from the disruptor; d, d 32 (m) is the average diameter of the bubbles Sauter flowing out from the bubble breaker; q is calculated according to mass balance G And Q is equal to G0 The following relationship is provided:
for the study of the present invention, ΔP < P m Thus, Q G ≈Q G0 . For convenience of description, the flow rates of the gas entering and exiting are referred to as Q G And (3) representing. Preliminary calculations indicate that the gas-liquid interface energy value is negligible relative to the liquid kinetic energy value. This term is ignored first and then checked by calculation. Thus, equation (5) can be reduced to:
s200, calculating liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
according to the assumption of closed cycle, the flow of the inlet and outlet liquid is equal, so there is
Q L ＝U L S 1 (1-φ G ) (64)
Wherein the gas content in the bubble breaker phi G Can be calculated as follows:
from formulas (8) (9):
obviously U L Is the apparent velocity of the gas-liquid mixture in the bubble breaker. Substituting equation (10) into equation (7) yields:
from equation (11), the liquid flow rate Q at the nozzle diameter due to the gas input can be calculated L But the form is more complex, and the design is reasonably simplified according to the actual situation of the project. From equation (7):
calculations indicate that under the conditions studied in the present invention, Q L <<Q G . Equation (11) can be simplified as:
this gives:
in fact, from the ideal state equation, the following relationship exists:
substituting equation (15) into equation (14) yields:
from equation (16), it can be seen that: bubble breaker cross-sectional area S 1 For liquid circulation flow rate Q L The effect is greater;
as a result of:
v in N Is the flow rate at the nozzle;
when V is N At a certain time, it is obtainable by formulas (16) and (17):
when D is N At a certain time, it is obtainable by formulas (16) and (17):
from formulae (10) and (16):
the above is based on the whole qiQ under dynamic conditions L Is a rough calculation of (a). Further according to known V N Determining diameter D N (when D N V can also be obtained at a fixed time N )。
S300, calculating energy dissipation rate epsilon of gas-liquid intensive mixing area mix ；
d 32 Energy dissipation ratio epsilon of gas-liquid intensive mixing area in bubble breaker mix Closely related. According to the first law of thermodynamics:
in the above, L mix The length of a gas-liquid intensive mixing zone in bubble breaking is m; lambda (lambda) 1 Is the ratio of the gas-liquid volume flow rate (lambda) 1 ＝Q G /Q L )。K 1 Is the ratio of the diameter of the bubble breaker nozzle to the diameter of the breaker (K 1 ＝D N /D 1 )。
Evans et al have derived L based on the principle of conservation of kinetic energy mix But is not applicable to the cases involved in the studies of the present invention and thus needs to be deduced again. The research of the invention considers that L mix Depending on the length of the decay of the highest flow rate of liquid in the bubble breaking zone until it disappears. The highest flow velocity of the liquid is in the attenuation process, and the central line speed U of the liquid is the same jm The attenuation law of (2) is not influenced by the disturbance of surrounding bubbles, and accords with the following attenuation law:
in equation (22), x is the horizontal distance from the bubble breaker core to the maximum speed. When U is jm Decaying to the apparent speed U of the gas-liquid mixture L At this point, the high velocity disappears, after which a uniform gas-liquid mixture stream will be formed. Thus, L mix Is U (U) jm ＝U L X value at that time.
Namely:
the equation (23) can be simplified to obtain:
substituting equation (24) into (21) and simplifying to obtain:
combining (16) (20) and equation (25) to calculate ε mix 。
S400, calculating the bubble size of micro bubbles in the MIHA;
microbubbles d in MIHA 32 Calculating 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, d max Is the maximum diameter of the bubble; mu (mu) L Is hydrodynamic viscosity;
s500, calculating the phase boundary area of the micro gas-liquid system;
the phase boundary area is calculated according to the following formula:
example 2
This example specifically illustrates a phase boundary area control model constructed based on the method of example 1.
The phase boundary area control model was obtained based on the modeling method of example 1 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 the operating pressure, operating temperature, air supply pressure difference Δp, and ventilation Q are studied for specific reactor structures and reaction systems G Impact on phase boundary area.
The general calculation conditions are as follows:
diameter D of crusher 1 =0.02m; ratio K of diameter of bubble breaker nozzle to breaker diameter 1 ＝0.5；
Density ρ of residuum L ＝800Kg/m 3 ；
Interfacial tension sigma of residuum L The fitting formula is as follows:
σ L ＝[31.74-0.04775(T+273.15)]×10 -3 (N/m)；
dynamic viscosity of residuum mu L The fitting formula is as follows;
(1) The influence of the operating pressure on the phase boundary area a;
the calculation conditions are as follows:
ventilation Q G =80l/h; operating pressure P m =10 to 20MPa; air supply pressure difference Δp=6 MPa; gas temperature t=500℃.
As a result, as shown in FIG. 2, it can be seen that the operating pressure P m The influence on the gas-liquid phase boundary area a is small. The main reason is P m For liquid circulation flow rate Q L The influence of (2) is small. Analysis of P embodied in equation (16) above m For Q L The influence is known;
when P m When increasing, (P) m +ΔP) term increases
The term is reduced, eventually Q L Is subjected to P m The influence of (2) is minimal. In addition, Q L Is to determine d 32 Air content phi G The latter two determine the size of a by equation (29). Thus, the operating pressure P m The above effect on a is reasonable.
(2) Influence of the operating temperature on the phase boundary area a;
the calculation conditions are as follows:
ventilation Q G =80l/h; operating pressure P m =14 MPa; air supply pressure difference Δp=6 MPa; the gas temperature t=400 to 500 ℃.
The effect of operating temperature on a is shown in FIG. 3; it can be seen that the gas-liquid phase interfacial area a increases with increasing operating temperature. The main reason is that: when the operating temperature of the system is singly changed, the gas-liquid phase interfacial area a is only limited by d 32 Is a function of (a) and (b).
(3) The influence of the air supply pressure difference deltap on the phase boundary area a;
the calculation conditions are as follows:
density ρ of residuum L ＝800Kg/m 3 The method comprises the steps of carrying out a first treatment on the surface of the Operating pressure P m =14 MPa; the air supply pressure difference delta P=1 to 10MPa; gas temperature t=450℃.
The results are shown in FIG. 4 (ventilation 80L/h); it can be seen that the pressure difference of the air supply is increased, the energy dissipation rate of the bubble breaker is increased, and the gas-liquid phase interfacial area is reduced. When the energy dissipation rate of the bubble breaker is increased, the diameter of the bubble is reduced, and the increase of the air supply pressure difference tends to accelerate the flow of liquid in the reactor due to the full pneumatic mode, which produces two results: on the one hand, the enhanced turbulence of the liquid in the bubble breaker leads to an increased energy dissipation rate and a decreased bubble; on the other hand, the residence time of the bubbles in the reactor is shortened, resulting in a reduction in the gas content, and the latter effect is more pronounced, as a result of which the gas-liquid phase interfacial area is reduced.
(4) Ventilation Q G Influence on the phase boundary area a;
the calculation conditions are as follows:
ventilation Q G =1 to 100L/h; operating pressure P m =14 MPa; the air supply pressure difference delta P=0.1-10 MPa; gas temperature t=500℃.
The results are shown in FIG. 5; it can be seen that the gas-liquid phase interfacial area a in the reactor increases with increasing ventilation, approximating a linear relationship.
Claims (2)
1. The modeling method of the phase boundary area regulation model under the MIHA pure pneumatic operation condition is characterized by comprising the following steps of:
s100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
under purely pneumatic operating conditions, the liquid flow rate Q L <<Gas flow rate Q G Before the gas is not introduced, the bubble breaker is filled with static reaction liquid; the system liquid is in closed cycle, i.e. the liquid amount does not change in the whole process; part of the liquid is forced to enter the outer circulation pipeline of the bubble breaker due to the entering of the gas; setting the length of the bubble breaker as L and the diameter as D 1 Cross-sectional area S 1 ＝πD 1 2 4; nozzle diameter D N ；
The calculation preconditions are as follows:
(1) Steady state operation, operating pressure P m Constant;
(2) The change of potential energy of liquid and the change of gas pressure in the bubbles caused by interfacial tension of the bubbles are ignored because of higher actual operation pressure;
(3) Since the gas density is much smaller than the liquid, the kinetic energy of the input gas is ignored;
taking a bubble breaker as a control body, and performing energy balance under a steady-state condition; under pneumatic conditions, the pressure is P G0 The volume flow is Q G0 Is constant at P m When the bubble breaker is used, part of static pressure energy is released by the gas and is converted into liquid kinetic energy and bubble surface energy; the static pressure energy released by the gas is equivalent to the work W of the gas on the system G According to the work definition, it can be seen that:
Q G the gas flow in the bubble breaker is obtained according to an ideal gas state equation:
in the formula (2), ρ G0 And M A The density and the molar mass of the gas entering the crusher are respectively; r and T are respectively a gas constant and a gasA bulk temperature;
substituting formula (2) into formula (1) and integrating to obtain:
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, W is G < 0, i.e. the mechanical energy of the gas will be reduced after it enters the bubble breaker; due to bubble breaker operating pressure P m Constant, neglecting the gravitational potential energy of the liquid, and converting the reduced mechanical energy of the gas into liquid kinetic energy and bubble interface energy; thus, the following formula (3) (4) can be obtained:
the left side of the equal sign of equation (5) is the reduction of the static pressure energy of the gas, namely-W G The method comprises the steps of carrying out a first treatment on the surface of the The right two terms of the equal sign of the equation (5) are respectively liquid kinetic energy and gas-liquid interface energy; wherein ρ is L Sum sigma L Liquid density and interfacial tension, respectively; u (U) L Is the linear velocity of the liquid flowing out of the disrupter; d, d 32 An average diameter of the air bubbles Sauter flowing out from the air bubble breaker; q is calculated according to mass balance G And Q is equal to G0 The following relationship is provided:
due to DeltaP < P m Thus Q G ≈Q G0 The method comprises the steps of carrying out a first treatment on the surface of the Neglecting the gas-liquid interface energy value relative to the liquid kinetic energy value, the equation (5) is simplified to:
s200, calculating liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
since the liquid entering and exiting the crusher is in closed cycle, i.e. the flow rates of the liquid entering and exiting are equal, the liquid entering and exiting are:
Q L ＝U L S 1 (1-φ G ) (8)
wherein the gas content in the bubble breaker phi G Calculated as follows:
from formulas (8) (9):
U L substituting equation (7) for the apparent velocity of the gas-liquid mixture in the bubble breaker, it is possible to obtain:
from equation (11), the liquid flow rate Q at the nozzle diameter due to the gas input can be calculated L From equation (7):
under purely pneumatic operating conditions, Q L <<Q G Then equation (11) is reduced to:
this gives:
from the ideal state equation, the following relationship exists:
substituting equation (15) into equation (14) yields:
from equation (16), it can be seen that: bubble breaker cross-sectional area S 1 For liquid circulation flow rate Q L The effect is greater;
as a result of:
v in N Is the flow rate at the nozzle;
when V is N At a certain time, it is obtainable by formulas (16) and (17):
when D is N At a certain time, it is obtainable by formulas (16) and (17):
from formulae (10) and (16):
thereby completing the Q under the pure pneumatic condition L Is determined by the estimation of (a);
s300, calculating energy dissipation rate epsilon of gas-liquid intensive mixing area mix ；
According to the first law of thermodynamics:
in the above, L mix The length of a gas-liquid intensive mixing zone in bubble breaking is m; lambda (lambda) 1 Lambda is the ratio of the gas to the liquid volume flow 1 ＝Q G /Q L ；K 1 K is the ratio of the diameter of the bubble breaker nozzle to the diameter of the breaker 1 ＝D N /D 1 ；
L mix In connection with the length of the decay of the liquid maximum flow velocity in the bubble breaking zone until it has disappeared, the liquid maximum flow velocity during its decay, the central line velocity U jm The attenuation law of (2) is not influenced by the disturbance of surrounding bubbles, and accords with the following attenuation law:
in equation (22), x is the horizontal distance of the bubble breaker core to the maximum speed; when U is jm Decaying to the apparent speed U of the gas-liquid mixture L At this time, the high velocity disappears, after which a uniform gas-liquid mixture stream will be formed; thus, L mix Is U (U) jm ＝U L The value of x at that time, namely:
the equation (23) can be simplified to obtain:
substituting equation (24) into (21) and simplifying to obtain:
combining (16) (20) and equation (25) to calculate ε mix ；
S400, calculating the bubble size of micro bubbles in the MIHA;
microbubbles d in MIHA 32 Calculating 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)
wherein d min Is the minimum diameter of the bubble; d, d max Is the maximum diameter of the bubble; mu (mu) L Is hydrodynamic viscosity;
s500, calculating the phase boundary area of the micro gas-liquid system;
the phase boundary area is calculated according to the following formula:
2. a reactor designed according to the method of claim 1.
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