CN107563051A - Micro-interface enhanced reactor bubble scale structure imitates regulation-control model modeling method - Google Patents
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Abstract
The present invention relates to a kind of micro-interface enhanced reactor bubble scale structure to imitate regulation-control model modeling method, with micro-interface enhanced reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble Sauter average diameters d32Its numerical relation is constructed for dependent variable；And it is theoretical based on Kolmogorov Hinze, construct micro-interface enhanced reactor largest air bubbles diameter dmax, minimum bubble diameter dminRelation between reactor parameter.The method of the present invention contacts reactor bubble scale with the structural parameters, operating parameter and physical parameter of reactor with specific numerical relation together with, design for reactor has directive significance, and it is applicable to a variety of reactors, versatility is good, the bubble scale regulation-control model built using the modeling method of the present invention, further the maximization target that course of reaction efficiency thing is imitated can be obtained by adjusting structural parameters and the operating parameter of reactor, or under given reaction target and energy and material consumption, design efficient structure of reactor.
Description
Technical field
The invention belongs to chemical industry manufacture, reactor, modeling technique field, and in particular to a kind of micro-interface enhanced reactor gas
Steep yardstick structure effect regulation-control model modeling method.
Background technology
The heterogeneous reactions such as oxidation, hydrogenation, chlorination are widely present in chemical process, its Global reaction Rate typically by
It is formed on mass transport process.It is common that the mass transfer rate of gas liquid reaction is mainly accumulated a by liquid side (or gas side) mass tranfer coefficient and gas liquid film
Influence.There are some researches show a is bigger to the influence degree of volume transmission quality coefficient, and easily regulation and control.Therefore, increase a is considered as carrying
The high particularly effective approach by mass transfer limited gas liquid reaction system reaction efficiency.
Bubble Sauter average diameters d32It is one of the key parameter for determining a sizes, they are mainly between by bubble and gas-liquid
Two-phase Interaction Force influences.Bubble coalescence and division are then the result of above two active force respectively, and it is straight to influence bubble
The size in footpath.Therefore, the meso-scale behavior of bubble coalescence and rupture as bubble, it is the profound cause for determining a sizes.Close
It is long-standing in the research of bubble coalescence and disruptive behaviour, generally believe energy absorbing device and d32It is important influence factor.Thing
In reality, d32A and volume transmission quality coefficient size can be influenceed, is the central factor for determining gas-liquid Global reaction Rate[1].Research is aobvious
Show, work as d32When being gradually reduced, volumetric mass transfer rate gradually increases；Particularly work as d32During less than 1mm, volumetric mass transfer rate is with d32
Reduction comparatively fast to increase similar to exponential form.Therefore, d is reduced as much as possible32Gas-liquid mass transfer can be strengthened and finally increased
Global reaction Rate.
Bubbling reactor and stirring-bubbling reactor are industrial most traditional and conventional gas-liquid reactors.As PX is aoxidized
TA processed tower bubbling reactor, bubble diameter are typically larger than 10mm, or even a few Centimeter Levels, and its mass transfer interfacial area extremely has
Limit, it is therefore necessary to reactor is made very big, to improve Global reaction Rate, while liquid must be promoted by increasing air-blowing amount
Body turbulent flow, improves gas holdup, and then increases interfacial area, but this measure necessarily reduces the utilization rate of oxygen in air, increase compression
Acc power and exhaust emissions, cause energy consumption transition and loss of material and environmental pollution.In terms of turbulent flow dynamics angle, traditionally use
Obtain most widely to be formed mostly in stirring-bubble type gas-liquid reactor and have an impact to bubble macroscopic motion but bubble breaking is acted on
Little big whirlpool, bubble can not be crushed effectively, therefore bubble diameter is bigger than normal, and mass transfer area is limited, so that reaction efficiency is relatively low.To be strong
Change gas-liquid mass transfer, tower bubbling reactor typically sets up the internals such as gas distribution grid, static mixer to strengthen mixing, and stirs
Kettle then needs to install the structures such as agitating paddle or the inner cylinder of different structure, to increase the air content of liquid layer.Nevertheless, both react
Bubble diameter in device is usually 5~20mm, and the phase contact area in the unit volume provided is extremely limited, is generally less than
100m2/m3, therefore reaction efficiency can not possibly obtain breakthrough raising.Therefore, industrially frequently by HTHP and increasing tolerance
To improve gas holdup and phase contact area, but this energy consumption, material consumption and reaction selectivity to course of reaction has great negative shadow
Ring.
Because the micro- crushing technology for researching and developing bubble is particularly significant, therefore most in the past 10 years, English, U.S., moral, Deng states university with
Research institution begins to focus on and researched and developed ultra-fine bubbler techniques[2-11], but its achievement in research has following common defects：
(1) though can obtain the bubble of a certain amount of micron order yardstick using means such as Mechanical Crushing, fluid impact, ultrasounds,
Gas liquid ratio the ratio between (gas volume with liquid volume) is too low, and generally below 1%, the upper limit is no more than 5%.In addition, produce microbubble
Equipment energy consumption and manufacturing cost it is too high.
(2) liquid phase is still not based on both at home and abroad as continuous phase and the microbubble architectural characteristic of high turbulence, proposes system
The micro-interface mass transfer enhancement of change is theoretical, microbubble test and characterizing method, micro-interface enhanced reactor structure effect regulate and control theoretical and phase
Close mathematical modeling.
For these reasons, though there is fragmentary application experiment result to deliver, there has been no the commercial Application of scale to report,
Especially chemical industry manufacturing field application substantially also in space state.
The Chemical Manufacture of current era, based on innovation, green, the overall consideration of environmental protection, its survival and development is depended on to material
Material is significantly innovated with process technology.Reaction is improved with the Atom economy of separation process to reducing energy consumption, material consumption, enhancing the competitiveness
It is most important.Based on this, it is proposed that " micro-interface mass transfer enhancement reaction-finely separate integrated system " new technology, it is intended to from most
Basic ultra-fine gas-liquid particle characteristics research is set out, and is solved under high turbulence state in ultra-fine grain system, micro-interface chemistry
Theory, technology in reactor involved by the structure such as flow of fluid, mass transfer, reaction, energy conversion effect regulation and control overall process are asked with application
Topic.
Ultra-fine gas-liquid particle of the present invention refers to ultra-fine bubble (or fine droplets), is that particle equivalent diameter is in
1μm≤d0＜ 1mm micron order gas-liquid particle.In reaction system, ultra-fine gas-liquid particle forms ultra-fine interface (or micro- boundary
Face), the formation at ultra-fine interface significantly enhances mass transfer and reaction rate, especially by mass transfer limited reaction system.
, it is emphasized that classical gas-liquid mixed theory is generally basede on millimeter-Centimeter Level gas-liquid particle characteristic, presently the most
Rational method is multiple dimensioned minimum energy principle (EMMS)[12].Current research work mostly is anti-for traditional gas-liquid
Answer bubble on the grade in device[13,14], seldom it is related to ultra-fine grain system.Mixing, mass transfer for ultra-fine grain system with
Response characteristic, it is necessary to establish new computation model, test and characterizing method, and structure effect regulation-control model, must be studied newly for this
Device structure, energy input form and translative mode, so as to form the brand-new calculating for being suitable for ultra-fine grain reaction system
Software and hardware platform, offer technology is attained a new height with equipping support for the process industrial production technology in China.
In the prior art for d32The research of algorithm typically has two kinds：
1.Wherein niRepresent bubble number, diRepresent bubble diameter；The shortcomings that this algorithm is to need to know
The alveolate diameter of institute and bubble number in system, this can not accomplish at present, and this formula does not include reactor yet
Structural parameters, operating parameter and physical parameter, be not truly for the directive significance that is designed without of reactor
Structure imitates regulation-control model；
2. d32=α dmax, proportionality coefficient α in this formula, come out by empirical estimating, can only be directed to some specific
System, and error is larger.
So-called structure effect regulation and control mathematical modeling, refer to the reaction efficiency (efficiency and thing effect) of ultra-fine gas-liquid particle reaction system
Mathematically associate with system physicochemical property, micro-interface characteristic, mass transfer characteristic and structure of reactor, can lead to so as to realize
Adjustment structural parameters and operating parameter are crossed to obtain the maximization target of course of reaction efficiency thing effect, or in given reaction target
Under (task) and energy and material consumption, efficient structure of reactor is designed.And for micro-interface enhanced reactor, work in this respect
Work is still blank in the world.
Bibliography
[1]Levenspiel O.Chemical Reaction Engineering[M].Wiley New York etc.,
1972.
[2]Xu JH,Li SW,Chen GG,LuoG..Formation of monodispersemicrobubbles in
a microfluidic device[J].AIChE Journal,2006,52(6):2254-2259.
[3]Li P and Tsuge H.Ozone transfer in a new gas-induced contactor
with microbubbles[J].Journal of Chemical Engineering of Japan,2006,39(11):
1213-1220.
[4]Muroyama K,Imai K,Oka Y,Hayashi J,Mass transfer properties in a
bubble column associated with micro-bubble dispersions[J].Chemical
Engineering Science,201,100:464-473.
[5]Maeda Y,Hosokawa S,Baba Y,Tomiyama Akio.Generation mechanism of
micro-bubbles in a pressurized dissolution method[J].Experimental Thermal and
Fluid Science,2015,60:201-207.
[6]Hasegawa H,Nagasaka Y,Kataoka H.Electrical potential of
microbubble generated by shear flow in pipe with slits.Fluid Dynamics
Research,2008,40(7-8):554-564.
[7]Weber J and Agblevor F.Microbubble fermentation of
Trichodermareesei for cellulase production[J].Process Biochemistry,2005,40
(2):669-676.
[8]Rehman F,Medley GJ,Bandulasena H,Zimmerman WB.Fluidic oscillator-
mediated microbubble generation to provide cost effective mass transfer and
mixing efficiency to the wastewater treatment plants[J].Environmental
research,2015,137:32-39.
[9]Stride E and Edirisinghe M.Novel microbubble preparation
technologies[J].Soft Matter,2008,4(12):2350.
[10]Druzinec D,Salzig De,Kraume M,Czermak P.Micro-bubble aeration in
turbulent stirred bioreactors:Coalescence behavior in Pluronic F68containing
cell culture media[J].Chemical Engineering Science,2015,126:160-168.
[11] Li Baozhang, Shang Longan, research [J] the Northwest Universitys journal of the Jiang Xinzhen circulation flow reactors of falling injecting type is (certainly
Right science version) .1989,04:65-69.
[12]Chen JH,Yang N,Ge W,Li JH.Stability-driven structure evolution:
exploring the intrinsic similarity between gas-solid and gas-liquid systems
[J].Chinese Journal of Chemical Engineering.2012,20(1):167-177.
[13]Hinze JO.Fundamentals of the hydrodynamic mechanism of splitting
in dispersion processes[J].AIChE Journal.1955,1(3):289-295.
[14]Zhong S,Zou X,Zhang ZB,Tian HZ.A flexible image analysis method
for measuring bubble parameters[J].Chemical Engineering Science,2016,141(17):
143-153.
The content of the invention
A kind of it is an object of the present invention to the defects of overcoming prior art, there is provided micro-interface enhanced reactor bubble scale
Structure imitates regulation-control model modeling method.
To achieve the above object, the present invention adopts the following technical scheme that：
A kind of micro-interface enhanced reactor bubble scale structure imitates regulation-control model modeling method, including：
(1) with micro-interface enhanced reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble
Sauter average diameters d32For dependent variable, d is establishedmax、dminAnd d32Between relation；Comprise the following steps that：
If x, m, n be respectively bubble diameter in reactor gas-liquid system, bubble diameter geometry natural logrithm average and
Standard deviation, obtain bubble diameter x probability density function：
Bubble diameter meets bubble Sauter average diameters d during this distribution32For：
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore lnx mathematic expectaion (arithmetic mean of instantaneous value) is：
Bubble diameter probability density figure is drawn according to bubble diameter x probability density function, whenWhen, probability density is most
Greatly；First derivative i.e. herein is 0：
Equation (3) substitution (1) is obtained into equation (4)：
It can be obtained by (3), (4)：
Due to：
It can be obtained after equation (1) is substituted into (6) and abbreviation：
Order：Then above formula is reduced to：
Equation (8) left end is error function, and the difference of the limit of integration is with the difference of standard error function, by formula (5) point
Above-mentioned range of integration is not substituted into, and can be obtained after equation (8) is converted into standard error function：
In equation (9), erf () is error function；
For the error function of following form：
Its approximate calculation can use series expansion.Classical Taylor series expansion, its convergence rate is compared with Chebyshev
(Chebyshev) series is slow, but has relatively simple quantic, therefore is widely adopted.For engineering research,
Acquisition form is relatively simple, the succinct expression that error can be received by engineering field, without pursuing error in mathematical meaning
Minimum accurate expression.Taylor series expansion is different according to the span of error function independent variable and uses different forms,
Such as：
As z≤4, erf (z) is deployable to be：
Due to：
Work as dmax/dminFor 1000 when：
And according to equation (11)：
Therefore, when：
I.e.：
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is relevant, and n is by dmax/dminSize system
About；Bubble diameter cumulative probability density g (n) is built to investigate n and dmax/dminInfluence to equation (9) establishment condition, makes bubble
Particle-size accumulation probability density g (n) is：
Draw g (n)~n relation curves；Acquisition ensure equation (9) set up n can span and dmax/dminPass
System；
The equal sign condition of inequality (16) is taken, i.e.,：
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows：
(2) it is theoretical based on Kolmogorov-Hinze, structure micro-interface enhanced reactor largest air bubbles diameter dmax, it is minimum
Bubble diameter dminRelation between reactor parameter；
For ultra-fine bubble system, the rupture of bubble and the formation of new bubble betide the larger bubble breaking areas of ε,
Energy is transmitted to gas-liquid interface due to turbulence vortex and efficiency be present, the minimum turbulence vortex yardstick of bubbles burst can be made be
11.4~31.4 times of Kolmogorov yardsticks, it is assumed that this multiplying power is 11.4, is more than its chi because turbulence vortex is only capable of broken diameter
The bubble of degree, therefore, bubble diameter minimum value dminIt is consistent with the turbulence vortex yardstick, i.e.,：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Theoretical, the largest air bubbles diameter d based on Kolmogorov-HinzemaxDetermined by following formula (22)：
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；
WecritFor the critical weber numbers of bubble breaking；
The critical weber numbers We of bubble breaking used by difference researchcritIt is different.This is mainly weber numbers and bubble week
The flow pattern enclosed is relevant, and the more difficult quantitative description of flow pattern.The resonance theory based on bubble breaking determines We in the present inventioncrit：
Wherein, α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer, and bubble is got over
It is small, select α for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
Now：
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Preferably, the energy absorbing device ε is obtained in the following way：
Step 100：It is micro-interface enhanced reactor by the total energy absorbing device ε of micro-interface enhanced reactor computation partition
The summation of interior three different zones energy absorbing devices, include the energy absorbing device ε of reactor body area bubbling areaR, gas-liquid crushes
The ε in areamixAnd the ε in gas liquid outlet areapl；
Step 110：Wherein, the energy absorbing device ε of reactor body area bubbling areaRCalculate in the following way：
In gas reactor sparging process, system is done work according to bubble, εRIt is expressed as：
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120：Calculate the ε of gas-liquid fracture areamix：
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gas
Mass flow, and the unit of energy absorbing device is unified for W/Kg, it is as follows to obtain calculation formula：
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid
Mixture pressure, Pa；λ1For the ratio between gas-liquid volume flow：K1For nozzle diameter and the ratio of bubble breaking area diameter, K1=DN/
D1；S1For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow in reactor,
m3/s；
λ1=QG/QL (27)
Step 121：Calculate bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1：
Ignore the pipe friction loss of bubble breaking area, then：
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows：
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the actual ENERGY E obtained of system0For：
I.e.：
Obtained by formula (28) (31)：
Step 122：Calculate bubble breaking section length Lmix：
LmixDetermined, or be determined as follows by measuring the inside pipe wall pressure jump of gas-liquid fracture area：
Wherein：PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vN
For the effluxvelocity of jet orifice, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHPushed away by Bernoulli equation：
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZCalculated by following formula：
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxFor jet orifice jet velocity and gas-liquid fracture area gas
The result of the Vector modulation of liquid mixture flow velocity, U is calculated using following formulae,max：
Formula (34) (36) is substituted into formula (33), and can be obtained after abbreviation：
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. work as Lmix＜ LbWhen, using the result of calculation of formula (37) as LmixActual numerical value；
2. work as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then：
Lmix=Lb (38)
Step 130：Calculate the ε in gas liquid outlet areapl；
The state assuming that bubble is evenly distributed in gas liquid outlet area, the energy dissipation rate ε in this regionplCalculated by following formula：
Structure of reactor ensures λ when designing1Adjustable extent is sufficiently large, is determined by experiment between reactor elementary structure parameter
Relation be K1=0.5, Lb=13D1；Substitute into foregoing corresponding expression formula and abbreviation can obtain：
Step 200：Determine εR、εmixAnd εplRespective numerical values recited；
Step 210：It is equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor,
Obtain：
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e., liquid circulation is total per hour
The ratio of volume and reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~
0.5；
From formula (43)：Then u1During increase, cross-sectional reactor area S0Also increase；Convolution (25) can
Know, now εRReduce；To be compared to the energy absorbing device of reactor different zones, it is assumed that：u1=3.0m/s；CL=20；H0
=1.5m；It can be obtained by formula (43), work as λ1When=0.1~0.5：
D0≈19D1 (44)
Selected D1Numerical value, simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed is calculated, it is determined that
With the energy absorbing device ε of gas-liquid fracture areamixCompare, reactor body area, the energy absorbing device in gas liquid outlet area are negligible not
Meter, i.e. εmix≈ε；The then mathematical relationship between the energy absorbing device ε of whole reactor and structure of reactor parameter, can be by formula
(26) calculate and determine, i.e.,：
The second object of the present invention is the bubble scale structure effect regulation-control model for providing above-mentioned modeling method structure.
Specifically, the bubble scale structure effect regulation-control model is as follows：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
In formula, QLFor liquid circulation volume flow in reactor；LmixFor bubble breaking section length；D1For bubble breaking Guan Zhi
Footpath；λ1For the ratio between gas-liquid volume flow, λ1=QG/QL；QGFor ventilation volume flow in reactor；P0For bubble breaker porch
The static pressure of liquid；P1Gas-liquid mixture pressure is exported for bubble breaking area；ε is energy absorbing device；μLFor hydrodynamic viscosity；σL
For surface tension of liquid；ρLFor fluid density.
A further object of the present invention is in the application in providing the above method and being designed in reactor.
According to required bubble Sauter average diameters d32Numerical value, the anti-of regulation-control model establishment is imitated by above-mentioned bubble scale structure
Answer device structural parameters, physical parameter, operating condition and bubble Sauter average diameters d32Relation, structural parameters are carried out to reactor
With the design of physical parameter so that structure of reactor parameter and physical parameter meet the number that bubble scale structure effect regulation-control model determines
Value relation.
The method of the present invention is applied to micro-interface enhanced reactor, and its core is bubble breaker.Bubble breaker
Principle is that the gas phase entrained by high-speed jet mutually hits carry out energy transmission, makes bubble breaking, its structural parameters has Lb、D1, in detail
Fine texture is shown in accompanying drawing 1, and in addition the other structures parameter of the reactor has D0、H0, specific reactor structure related content is
It is published in the patent CN10618766A of inventor's earlier application, is repeated no more in the present invention.
The present invention has the advantages that：
(1) regulation-control model is imitated using the bubble scale structure of the modeling method structure of the present invention, constructs dmax、dminAnd d32's
Direct calculated relationship, and d is no longer obtained by the way of experimental fit32Concrete numerical value, greatly reduce in the reactor should
With caused error；
(2) d of existing method structure32Model is directed to bubbling reactor (Bubble column, BC) and bubbling more
Gas-liquid system in stirred tank reactor (Bubbling-stirred reactor, BSR), or jet pump (gas-liquid
Jet bump, GLJB) in Air-Water system.And for industrial micro-interface reactor (MIR), then not necessarily it is applicable, its reason
It is：1. bubble breaking mechanism is different from above-mentioned reactor in MIR；2. it may relate to high viscosity in industrial gas-liquid reaction system
Liquid, and prior art (such as formula 46) does not consider liquid viscosity to d32Influence；And utilize the modeling method structure of the present invention
The bubble scale structure effect regulation-control model built is applicable to industrial micro-interface reactor (MIR), and its versatility is more preferable；
(3) regulation-control model is imitated using the bubble scale structure of the modeling method structure of the present invention, can be further anti-by adjusting
Structural parameters and the operating parameter of device is answered to react target to obtain the maximization target of course of reaction efficiency thing effect, or given
Under (task) and energy and material consumption, efficient structure of reactor is designed.
Brief description of the drawings
Fig. 1 is a kind of structure of reactor schematic diagram, for illustrating application of the modeling method of the present invention in reactor assembly；
Wherein 1- reactors, valve before 2- pumps, 3- circulating pumps, valve after 4- pumps, 5- fluid flowmeters, 6- heat exchangers, 7- bubble breakers, 8-
Temperature measurer, 9- down-comers, 10- gas traps, 11- gas flowmeters, 12- gas phase entrances, 13- pressure gauges, 14- liquid level gauges；D0- anti-
Answer device diameter, H0Initial liquid level height, D in-reactor1- bubble breaking pipe diameter, Lb- bubble breaking section length；
Fig. 2 is n and dmax/dminTo the influence curve figure of bubble diameter cumulative probability density；
Fig. 3 is the comparison of computational results curve map of prior art and the present invention.
Embodiment
Embodiment 1
The present embodiment illustrates the modeling method of bubble scale model of the present invention.
The method of the present invention, including：
(1) with micro-interface enhanced reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble
Sauter average diameters d32For dependent variable, d is establishedmax、dminAnd d32Between relation；Comprise the following steps that：
If x, m, n be respectively bubble diameter in reactor gas-liquid system, bubble diameter geometry natural logrithm average and
Standard deviation, obtain bubble diameter x probability density function：
Bubble diameter meets bubble Sauter average diameters d during this distribution32For：
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore lnx mathematic expectaion (arithmetic mean of instantaneous value) is：
Bubble diameter probability density figure is drawn according to bubble diameter x probability density function, whenWhen, probability density is most
Greatly；First derivative i.e. herein is 0：
Equation (3) substitution (1) is obtained into equation (4)：
It can be obtained by (3), (4)：
Due to：
It can be obtained after equation (1) is substituted into (6) and abbreviation：
Order：Then above formula is reduced to：
Equation (8) left end is error function, and the difference of the limit of integration is with the difference of standard error function, by formula (5) point
Above-mentioned range of integration is not substituted into, and can be obtained after equation (8) is converted into standard error function：
In equation (9), erf () is error function；
For the error function of following form：
Its approximate calculation can use series expansion.Classical Taylor series expansion, its convergence rate is compared with Chebyshev
(Chebyshev) series is slow, but has relatively simple quantic, therefore is widely adopted.For engineering research,
Acquisition form is relatively simple, the succinct expression that error can be received by engineering field, without pursuing error in mathematical meaning
Minimum accurate expression.Taylor series expansion is different according to the span of error function independent variable and uses different forms,
Such as：
As z≤4, erf (z) is deployable to be：
Due to：
Work as dmax/dminFor 1000 when：
And according to equation (11)：
Therefore, when：
I.e.：
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is relevant, and n is by dmax/dminSize system
About；Bubble diameter cumulative probability density g (n) is built to investigate n and dmax/dminInfluence to equation (9) establishment condition, makes bubble
Particle-size accumulation probability density g (n) is：
G (n)~n relation curves are drawn, as shown in Figure 2；For the gas-liquid system of determination, bubble size distribution is (by m and n
Determine) by dmax/dminInfluence；Work as dmax/dminOne timing, n should uniquely determine value, i.e. bubble size distribution is unique.
As shown in Figure 2：Ensure equation (9) set up n can span and dmax/dminIt is closely related, but as n → 0, n and dmax/
dminIt is unrelated；
The equal sign condition of inequality (16) is taken, i.e.,：
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows：
(2) it is theoretical based on Kolmogorov-Hinze, structure micro-interface enhanced reactor largest air bubbles diameter dmax, it is minimum
Bubble diameter dminRelation between reactor parameter；
For ultra-fine bubble system, the rupture of bubble and the formation of new bubble betide the larger bubble breaking areas of ε,
Energy is transmitted to gas-liquid interface due to turbulence vortex and efficiency be present, the minimum turbulence vortex yardstick of bubbles burst can be made be
11.4~31.4 times of Kolmogorov yardsticks, it is assumed that this multiplying power is 11.4, is more than its chi because turbulence vortex is only capable of broken diameter
The bubble of degree, therefore, bubble diameter minimum value dminIt is consistent with the turbulence vortex yardstick, i.e.,：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Theoretical, the largest air bubbles diameter d based on Kolmogorov-HinzemaxDetermined by following formula (22)：
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；
WecritFor the critical weber numbers of bubble breaking；
The critical weber numbers We of bubble breaking used by difference researchcritIt is different.This is mainly weber numbers and bubble week
The flow pattern enclosed is relevant, and the more difficult quantitative description of flow pattern.The resonance theory based on bubble breaking determines We in the present inventioncrit：
Wherein, α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer, and bubble is got over
It is small, select α for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
Now：
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Wherein, energy absorbing device ε is calculated in the following way：
Wherein, step 100：The total energy absorbing device ε of micro-interface enhanced reactor computation partition is strengthened for micro-interface
The summation of three different zones energy absorbing devices in reactor, include the energy absorbing device ε of reactor body area bubbling areaR, gas
The ε of liquid fracture areamixAnd the ε in gas liquid outlet areapl；
Step 110：Wherein, the energy absorbing device ε of reactor body area bubbling areaRCalculate in the following way：
In gas reactor sparging process, system is done work according to bubble, εRIt is expressed as：
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120：Calculate the ε of gas-liquid fracture areamix：
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gas
Mass flow, and the unit of energy absorbing device is unified for W/Kg, it is as follows to obtain calculation formula：
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid
Mixture pressure, Pa；λ1For the ratio between gas-liquid volume flow：K1For nozzle diameter and the ratio of bubble breaking area diameter, K1=DN/
D1；S1For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow in reactor,
m3/s；
λ1=QG/QL (27)
Step 121：Calculate bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1：
Ignore the pipe friction loss of bubble breaking area, then：
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows：
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the actual ENERGY E obtained of system0For：
I.e.：
Obtained by formula (28) (31)：
Step 122：Calculate bubble breaking section length Lmix：
LmixDetermined, or be determined as follows by measuring the inside pipe wall pressure jump of gas-liquid fracture area：
Wherein：PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vN
For the effluxvelocity of jet orifice, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHPushed away by Bernoulli equation：
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZCalculated by following formula：
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxFor jet orifice jet velocity and gas-liquid fracture area gas
The result of the Vector modulation of liquid mixture flow velocity, U is calculated using following formulae,max：
Formula (34) (36) is substituted into formula (33), and can be obtained after abbreviation：
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. work as Lmix＜ LbWhen, using the result of calculation of formula (37) as LmixActual numerical value；
2. work as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then：
Lmix=Lb (38)
Step 130：Calculate the ε in gas liquid outlet areapl；
The state assuming that bubble is evenly distributed in gas liquid outlet area, the energy dissipation rate ε in this regionplCalculated by following formula：
Structure of reactor ensures λ when designing1Adjustable extent is sufficiently large, is determined by experiment between reactor elementary structure parameter
Relation be K1=0.5, Lb=13D1；Substitute into foregoing corresponding expression formula and abbreviation can obtain：
Step 200：Determine εR、εmixAnd εplRespective numerical values recited；
Step 210：It is equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor,
Obtain：
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e., liquid circulation is total per hour
The ratio of volume and reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~
0.5；
From formula (43)：Then u1During increase, cross-sectional reactor area S0Also increase；Convolution (25) can
Know, now εRReduce；To be compared to the energy absorbing device of reactor different zones, it is assumed that：u1=3.0m/s；CL=20；H0
=1.5m；It can be obtained by formula (43), work as λ1When=0.1~0.5：
D0≈19D1 (44)
Selected D1Numerical value, simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed is calculated, it is determined that
With the energy absorbing device ε of gas-liquid fracture areamixCompare, reactor body area, the energy absorbing device in gas liquid outlet area are negligible not
Meter, i.e. εmix≈ε；The then mathematical relationship between the energy absorbing device ε of whole reactor and structure of reactor parameter, can be by formula
(26) calculate and determine, i.e.,：
Embodiment 2
The present embodiment illustrates the model of modeling method structure described in embodiment 1 in dioxy by taking the reactor shown in Fig. 1 as an example
Change the application in carbon and aqueous systems reactor.Fig. 1 structure of reactor can be the structure of existing micro-interface enhanced reactor, only adopt
Carries out parameter designing with the method for the present invention, the structure of reactor is repeated no more in of the invention.
The bubble scale structure effect regulation-control model built according to embodiment 1 is as follows：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
In formula, QLFor liquid circulation volume flow in reactor；LmixFor bubble breaking section length；D1For bubble breaking Guan Zhi
Footpath；λ1For the ratio between gas-liquid volume flow, λ1=QG/QL；QGFor ventilation volume flow in reactor；P0For bubble breaker porch
The static pressure of liquid；P1Gas-liquid mixture pressure is exported for bubble breaking area；ε is energy absorbing device；μLFor hydrodynamic viscosity；σL
For surface tension of liquid；ρLFor fluid density.
The model that embodiment 3 is selected mainly considers LmixLess than LbSituation because opposite situation is not common, compare pole
End.Structure of reactor parameter also needs to meet：λ1=0.1~0.5, K1=0.5, Lb=13D1；
For carbon dioxide and aqueous systems, when operating condition is：QL=2000L/h (5.56 × 10-4m3/ s), gas flow
QG=0.2QL, T=298K, PG0=1atm；And the physical parameter of liquid phase is in this system：ρL=1000kg/m3, μL=8.9 ×
10-4Pas, σL=7.197 × 10-4N/m；Reactor bubble breaking pipe diameter D1=0.02m；E0The energy of expression system input
Amount, i.e. rated power on circulating pump nameplate, take E0=1000W.
The bubble Sauter average diameters d that can be calculated according to operating condition and above-mentioned model32=0.426mm, and pass
The bubble mean diameter obtained under system process conditions is 1mm or so.As can be seen here, the bubble mean diameter of this reactor is than logical
Bubble mean diameter caused by paradoxical reaction device is small more than one times.
Levenspiel thinks that the Global reaction Rate of heterogeneous system can be expressed from the next：
Gas liquid reaction macroscopic view rate equation after abbreviation can be reduced to：
Tables 1 and 2 is the contrast situation of the parameters under same system different-grain diameter：
The parameter that the different-grain diameter drag formula of table 1 calculates
Three kinds of resistances (air film, liquid film, intrinsic) that the different-grain diameter drag formula of table 2 calculates
As shown in table 1, table 2, when bubble diameter is changed into original 1/10 and 1/2, gas liquid film integration does not increase
About 467 times and 9 times, Global reaction Rate increases about 4 times and 2 times respectively, and reacts resistance and be gradually transitioned into by liquid film controlled
By intrinsic reaction draught control.It can be seen that microbubble yardstick enhances gas-liquid mass transfer speed really.
Embodiment 3
The present embodiment illustrates the model of modeling method structure described in embodiment 1 in sky by taking the reactor shown in Fig. 1 as an example
Application in air-water system reactor, with existing prediction d32The superior part that model is compared.
For Air-Water system, prior art is typically using equation below prediction d32：
d32=0.65dmax (46)
Build the d of above formula and the inventive method structure32Predictor formula result of calculation contrast curve, as shown in Figure 3.By scheming
3 understand, when energy absorbing device ε is sufficiently small, (when ε is less than 10 (W/kg), this research and the result of calculation using formula (46) are basic
Unanimously；When ε gradually increases, both have different at prediction result：For Air-Water system, when ε is more than 10 (W/kg),
Formula (46) acquired results are relatively small, but error between the two is acceptable.
Formula (46) is disadvantageous in that：1st, the coefficient in the equation is obtained based on experimental fit, can not be associated
Reactor design parameter；2nd, d in equationmaxMathematic(al) representation obtained based on isotropic turbulence theory, and the theory is suitable
Premise is energy absorbing device infinity, and now, influence of the liquid viscosity to Air Bubble Size can be ignored.In recent years, entirely
The bubble size distribution of power spectrum has been studied, but form is more complicated, wherein some empirical parameters also be present, therefore is stilled need into one
Walk the reasonable determination of reduced form and model parameter.
And the method for the present invention is also based on isotropic turbulence theory and obtained, but pass through the probability to bubble size distribution
Statistical analysis, the relational expression obtained by rational Mathematical treatment, it is associated with bubble in liquid viscosity this pair of industrial reactors
The physical parameter that size has a major impact, can be as the basis of further commercial Application.
Claims (5)
1. a kind of micro-interface enhanced reactor bubble scale structure imitates regulation-control model modeling method, it is characterised in that including：
(1) with micro-interface enhanced reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble Sauter
Average diameter d32For dependent variable, d is establishedmax、dminAnd d32Between relation；Comprise the following steps that：
If x, m, n are respectively bubble diameter in reactor gas-liquid system, the average and standard of bubble diameter geometry natural logrithm
Difference, obtain bubble diameter x probability density function：
Bubble diameter meets bubble Sauter average diameters d during this distribution32For：
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore lnx mathematic expectaion (arithmetic mean of instantaneous value) is：According to
Bubble diameter x probability density function draws bubble diameter probability density figure, whenWhen, probability density is maximum；I.e.
First derivative herein is 0：
Equation (3) substitution (1) is obtained into equation (4)：
It can be obtained by (3), (4)：
Due to：
It can be obtained after equation (1) is substituted into (6) and abbreviation：
Order：Then above formula is reduced to：
Equation (8) left end is error function, and the difference of the limit of integration is with the difference of standard error function, by formula (5) generation respectively
Enter above-mentioned range of integration, and can be obtained after equation (8) is converted into standard error function：
In equation (9), erf () is error function；
For the error function of following form：
Approximate calculation is carried out using Taylor series expansion, Taylor series expansion is different according to the span of error function independent variable
And different forms is used, as z≤4, erf (z) is deployable to be：
Due to：
Work as dmax/dminFor 1000 when：
And according to equation (11)：
Therefore, when：
I.e.：
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is relevant, and n is by dmax/dminSize restriction；Structure
Bubble diameter cumulative probability density g (n) is built to investigate n and dmax/dminInfluence to equation (9) establishment condition, makes bubble diameter
Cumulative probability density g (n) is：
Draw g (n)~n relation curves；Acquisition ensure equation (9) set up n can span and dmax/dminRelation；
The equal sign condition of inequality (16) is taken, i.e.,：
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows：
(2) it is theoretical based on Kolmogorov-Hinze, structure micro-interface enhanced reactor largest air bubbles diameter dmax, minimum bubble
Diameter dminRelation between reactor parameter；
The minimum turbulence vortex yardstick that bubbles burst can be made is 11.4~31.4 times of Kolmogorov yardsticks, it is assumed that this multiplying power is
11.4, because turbulence vortex is only capable of bubble of the broken diameter more than its yardstick, therefore, bubble diameter minimum value dminWith the turbulence vortex
Yardstick is consistent, i.e.,：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Theoretical, the largest air bubbles diameter d based on Kolmogorov-HinzemaxDetermined by following formula (22)：
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；WecritFor gas
Bubble crushes critical weber numbers；
Resonance theory based on bubble breaking determines Wecrit：
Wherein, α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer, bubble with regard to smaller,
α is selected for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
Now：
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Bubble Sauter average diameters d is calculated according to formula (20), (21), (24)32。
2. according to the method for claim 1, it is characterised in that the energy absorbing device ε is obtained in the following way：
Step 100：It is three in micro-interface enhanced reactor by the total energy absorbing device ε of micro-interface enhanced reactor computation partition
The summation of individual different zones energy absorbing device, include the energy absorbing device ε of reactor body area bubbling areaR, gas-liquid fracture area
εmixAnd the ε in gas liquid outlet areapl；
Step 110：Wherein, the energy absorbing device ε of reactor body area bubbling areaRCalculate in the following way：
In gas reactor sparging process, system is done work according to bubble, εRIt is expressed as：
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120：Calculate the ε of gas-liquid fracture areamix：
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gaseous mass
Flow, and the unit of energy absorbing device is unified for W/Kg, it is as follows to obtain calculation formula：
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid mixed
Thing pressure, Pa；λ1For the ratio between gas-liquid volume flow：K1For nozzle diameter and the ratio of bubble breaking area diameter, K1=DN/D1；S1
For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow, m in reactor3/s；
λ1=QG/QL (27)
Step 121：Calculate bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1：
Ignore the pipe friction loss of bubble breaking area, then：
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows：
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the actual ENERGY E obtained of system0For：
I.e.：
Obtained by formula (28) (31)：
Step 122：Calculate bubble breaking section length Lmix：
LmixDetermined, or be determined as follows by measuring the inside pipe wall pressure jump of gas-liquid fracture area：
Wherein：PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vNTo penetrate
The effluxvelocity of head piece, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHPushed away by Bernoulli equation：
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZCalculated by following formula：
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxMixed for jet orifice jet velocity and gas-liquid fracture area gas-liquid
The result of the Vector modulation of compound flow velocity, U is calculated using following formulae,max：
Formula (34) (36) is substituted into formula (33), and can be obtained after abbreviation：
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. work as Lmix＜ LbWhen, using the result of calculation of formula (37) as LmixActual numerical value；
2. work as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then：
Lmix=Lb (38)
Step 130：Calculate the ε in gas liquid outlet areapl；
The state assuming that bubble is evenly distributed in gas liquid outlet area, the energy dissipation rate ε in this regionplCalculated by following formula：
Structure of reactor ensures λ when designing1Adjustable extent is sufficiently large, the pass being determined by experiment between reactor elementary structure parameter
It is for K1=0.5, Lb=13D1；Substitute into foregoing corresponding expression formula and abbreviation can obtain：
Step 200：Determine εR、εmixAnd εplRespective numerical values recited；
Step 210：It is equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor, obtains
Arrive：
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e. liquid circulation cumulative volume per hour
With the ratio of reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~0.5；
From formula (43)：Then u1During increase, cross-sectional reactor area S0Also increase；Knowable to convolution (25), now
εRReduce；To be compared to the energy absorbing device of reactor different zones, it is assumed that：u1=3.0m/s；CL=20；H0=1.5m；
It can be obtained by formula (43), work as λ1When=0.1~0.5：
D0≈19D1 (44)
Selected D1Numerical value, simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed is calculated, it is determined that and gas-liquid
The energy absorbing device ε of fracture areamixCompare, reactor body area, the energy absorbing device in gas liquid outlet area can be neglected, i.e. εmix
≈ε；The then mathematical relationship between the energy absorbing device ε of whole reactor and structure of reactor parameter, it can be calculated by formula (26) true
It is fixed, i.e.,：
。
3. the bubble scale structure effect regulation-control model of claim 2 methods described structure, it is characterised in that the bubble scale structure of structure
It is as follows to imitate regulation-control model：
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
In formula, QLFor liquid circulation volume flow in reactor；LmixFor bubble breaking section length；D1For bubble breaking pipe diameter；
λ1For the ratio between gas-liquid volume flow, λ1=QG/QL；QGFor ventilation volume flow in reactor；P0For bubble breaker porch liquid
The static pressure of body；P1Gas-liquid mixture pressure is exported for bubble breaking area；ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor
Surface tension of liquid；ρLFor fluid density.
4. application of the methods described of claim 1 or 2 in reactor design.
5. application according to claim 4, it is characterised in that according to required bubble Sauter average diameters d32Numerical value, lead to
Cross structure of reactor parameter, physical parameter, operating condition and bubble Sauter that above-mentioned bubble scale structure effect regulation-control model is established
Average diameter d32Relation, the design of structural parameters and physical parameter is carried out to reactor so that structure of reactor parameter and physical property
Parameter meets the numerical relation that bubble scale structure effect regulation-control model determines.
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