Latest / Mechanical Engineering Made Simple / (#86) Industrial Mixing Dimensionless Numbers and Scale-Up

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(#86) Industrial Mixing Dimensionless Numbers and Scale-Up · Mechanical Engineering Made Simple

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  Welcome back, design chuckies to mechanical engineering made
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  simple. Great to be back.
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  Today we are diving deep into a topic that honestly most people
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  never think about, but it it basically dictates the quality
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  and yield of products across, well, the entire chemical
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  industry. We're talking about industrial
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  mixing. That's right.
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  And if you think mixing is just, you know, dropping a blender in
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  a tank and hitting on, you're in for a surprise.
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  We're moving way past basic stirring today.
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  We're really peeling back the layers on the the rigorous
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  engineering correlations that govern how quickly something
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  blends, how you suspend solids, and this is the big one, how you
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  manage complex chemical reactions inside that tank.
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  And the sources for this deep dive are They're pretty meaty.
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  We've pulled from a big industry handbook on mixing all the
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  design rules, the correlations, the stuff engineers are actually
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  using every day. It's dense for sure, but our
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  mission really for you, the listener, is to distill this
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  down. We want to pull out the critical
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  metrics, things like dimensionless blend time, just
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  suspended speed, and yes, the famous dam color number.
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  The goal is to arm you with what you need to design or rate
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  mixing equipment so you don't get completely overwhelmed by
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  the fluid dynamics. Exactly, and so you can spot the
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  big failure modes before they happen.
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  OK, let's unack this. We should robably start with the
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  simplest duty, just blending fluids.
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  Makes sense. Let's look at standard agitated
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  vessels. We'll focus on Newtonian fluids
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  mostly in the turbulent regime. So Reynolds number over 200 or
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  somewhere in that transitional zone?
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  Yep, and when you're talking performance, the main
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  measurement is time. How long does it take to get
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  everything homogeneous? To make that useful across
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  different stales, we use the dimensionless blend time.
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  Which is quantified as N Theta 95.
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  Exactly. It's the impeller speed N times
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  the time it takes to get to 95% homogeneity, which is Theta 95.
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  And what's really interesting here is that in a fully
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  turbulent system, that number N Theta 95 is usually a constant.
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  So if you spin the impeller faster, the blend time gets
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  shorter and the product of the two stays the same.
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  That's the theory it sounds and simple.
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  But I'm guessing the real world has a twist.
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  Where does that simplicity fall apart it?
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  Falls apart when you look at the whole vessel.
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  That constant might hold true right under the impeller, but
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  some really important research, especially out of Cranfield,
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  showed a huge flaw and just relying on that.
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  What did they find? They found that the overall
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  blend time is actually controlled by the slowest moving
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  part of the fluid, and that's always in the least agitated
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  spot, typically the pocket of fluid right behind a baffle.
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  So you stick your probe in the middle of the tank and you think
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  you're done in 60 seconds, right?
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  But meanwhile that pocket behind the baffle is still, I don't
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  know, at 10% mixed. 5 minutes later, you've just made a bad
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  batch. Precisely that local blend time
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  behind the baffle shoots up as the Reynolds number drops.
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  It's a huge deal in the transitional regime.
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  You have to design for the worst case pocket, not the average.
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  OK, let's pivot to something that I found, well, truly
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  counterintuitive. The efficiency of the impeller
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  itself. Oh yeah, we're always told these
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  complex hydrofoils are way superior.
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  And for some things, like mass transfer, they are.
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  But for simple liquid blending in the turbulent regime, the
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  engineering conclusion is surprisingly blunt.
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  Which is all impellers of the same diameter are equally energy
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  efficient. Wait, wait.
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  I have to challenge that. Why would companies spend
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  millions developing proprietary blades if a simple flat turbine
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  is just as good for blending? Because the physics of turbulent
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  mixing are, well, relentless, the analysis shows that any
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  impeller of a given diameter will give you the same blend
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  time for the same power per unit mass.
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  There's a correlation that locks it in What's.
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  That look like. It's the power number piece of O
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  to the one third power times N Theta 95 times the ratio of the
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  impeller to tank diameter squared, and all of that equals
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  like 5.2. It's a constant.
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  So you're saying if I put a certain amount of power into the
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  tank, my mixing time is fixed no matter how fancy the blade is,
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  as long as the diameter is the? Same in that fully turbulent
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  zone, Yes, it's all about the power you put in now that all
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  changes in the transitional regime.
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  When things get thick and visible.
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  Exactly. There the blend time becomes
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  proportional to viscosity, and this is the key take away.
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  In that regime. Increasing the impeller diameter
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  gives you a much shorter blend time for the same power input,
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  so. Size matters more than shape
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  when you're fighting viscosity. That's a great practical nugget.
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  OK, so if blending is about flow patterns, let's move to where
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  mechanical design is just everything handling solids.
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  Right. We're moving from a single phase
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  to solid, liquid mixing. Yeah, the stakes get a lot
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  higher here. They really do.
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  You're not just trying to make it homogeneous, you're fighting
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  gravity to stop expensive catalysts or crystals from just
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  settling on the bottom and doing nothing.
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  You're trying to create a stable slurry.
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  A stable slurry? Exactly.
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  You have to suspend the solids, re suspend them if they've
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  settled, break up clumps and you know, maximize mass transfer at
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  the surface. And the difficulty there is tied
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  to all the physical properties, viscosity, density, particle
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  size and shape. It's a mess of variables.
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  It is the rule of thumb is simple.
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  Bigger, denser solids are harder to suspend, but engineering this
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  requires a specific number. And that gets us to the key
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  metric, the just suspended speed NJS.
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  NJS It's the absolute minimum impeller speed you need to lift
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  every last particle off the vessel bottom and to redict it.
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  Engineers lean very heavily on this vetoing correlation.
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  It's a workhorse. I remember that one.
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  It relies on a constant S right? And South seems to just absorb
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  all the geometric complexity. It really does.
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  NJS is super sensitive to that zeetering constant S, which
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  changes with impeller type, its diameter and its clearance from
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  the bottom. You change the clearance by an
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  inch, S changes and your required speed could jump up
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  significantly. And Speaking of geometry, the
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  shape of the vessel bottom itself is a huge factor.
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  Oh, it's transformative. Dished bottomed vessels are
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  strongly preferred. They eliminate the sharp corners
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  you get in a flat bottom tank. Which creates dead zones.
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  Exactly. Dead zones where the wall meets
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  the base. Solids just love to collect
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  their form a little fillet and completely drop out of
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  circulation. And you can't get them back.
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  You have to work much much harder to get them back.
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  The sources say your NJS is easily 10 to 20% higher in a
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  flat bottomed vessel just to fight those dead zones.
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  That's a huge power increase. Now let's make it even more
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  complicated. What if we add gas three phase
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  system? That's where, yeah, the
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  complexity just explodes. Gas bubbles interfere with the
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  liquid flow. They generally mean you need an
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  even higher NJS. You have to spin faster just to
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  fight the gas. But the sources warned about
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  something called a sudden collapse of the suspension.
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  That sounds bad. It's catastrophic.
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  Picture this. Your reactor is running fine,
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  solids are suspended. You start increasing the gas
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  flow to feed the reaction and you hit a critical point and
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  suddenly the whole system is dominated by the gas buoyancy.
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  The impellers flow is just overwhelmed.
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  All your expensive catalyst just crashes to the bottom of the
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  tank. The suspension is gone.
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  And your reaction dies. Or worse, if it's exothermic, it
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  runs away because you've lost all your heat transfer.
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  That really highlights why you need to do pilot test for these
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  systems. And that need for precision
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  brings us perfectly to chemical reactions, where mixing isn't
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  just about homogeneity, it can actually be the thing that
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  determines the rate of the chemistry itself.
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  We're talking about when mixing is basically in a race with the
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  chemistry, those fast mixing sensitive, competitive
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  consecutive reactions. Exactly.
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  Think about it like this. A+B makes your product R, but
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  your product R can also react with B to make a waste product
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  S. If you add B to the tank and it
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  doesn't mix instantly, you get these pockets of super high B
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  concentration. Before that B can find A.
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  It finds your precious product R and turns it into waste.
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  Your yield just tanks. So you need a way to quantify
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  that race, and that's where that dimensionless number comes in.
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  The damn cooler number for mixing tap.
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  Yes, damn. It's the ratio of the mixing
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  time Tau M divided by the reaction time Tau R.
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  If that number is large, say bigger than 10, that's a huge
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  red flag. It means mixing is the slow
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  step. It means you're actively
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  destroying your own product. And we learned earlier that you
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  absolutely can't use the bulk in time for this.
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  It has to be local mixing. It has to be.
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  The damage happens at the molecular level, right where you
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  add the reactant. You have to think about mixing
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  on three scales. There is macro mixing, that's
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  the bulk circulation. Then what?
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  Then meso mixing, the intermediate scale.
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  That's the initial breakup of the reactant plume as it enters
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  the tank. But the real decider, the hero
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  or the villain, is micro mixing. That's the smallest scale.
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  The absolute smallest? It's controlled by molecular
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  diffusion way down at the Kolmogorov scale in these tiny
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  little eddies. This is the stage that sets your
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  final product selectivity, because it's where the molecules
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  actually meet. If the stage is too slow, your
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  dam is high and your yield is garbage.
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  So if it all comes down to that tiny scale, what does that mean
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  for the person running the reactor?
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  Is it just about a bigger motor? It's more about placement.
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  The number one rule for these systems is always add your
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  reactive ingredient to the point of highest local turbulence, the
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  spot with the maximum energy dissipation, what engineers call
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  epsilon. So don't just dump it in the
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  top. Never.
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  If you feed it into a quiet zone, you guarantee poor micro
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  mixing and you're just throwing yield away.
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  And for scale up, you can't just make a bigger version of the
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  pilot reactor. No, that almost never works.
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  For these reactions. You have to scale up based on
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  maintaining a constant power per unit volume, or even better,
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  maintaining a constant turbulent energy dissipation rate right
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  there in the feed zone. That's what controls that
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  critical micromixing time. This gets even trickier with
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  heterogeneous reactions, right when you have multiple phases
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  and mass transfer is another layer.
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  That's right, Take a hydrogenation reaction.
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  You have hydrogen gas, a solid catalyst, and a liquid.
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  If you're mixing is bad, you can't get the gas bubble small
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  enough or spread them around. Your mass transfer rate, the KLA
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  is terrible. Where KLA is terrible, hydrogen
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  can't get from the bubble to the catalyst fast enough.
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  The reaction either crawls along or worse, if there's a side
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  reaction that likes high temperatures, start making junk.
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  And this is where changing the physical setup, the geometry can
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  be a total game changer. Absolutely.
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  The sources talk about cases where just switching to, say,
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  dual turbines or adding hardware to pull gas down from the
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  surface, it can dramatically boost the hydrogen uptake rate.
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  You turn a failing reaction into a successful one, not with
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  chemistry, but with pure mechanical engineering.
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  So if we pull all this together, our trip through industrial
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  mixing really shows that good design isn't guesswork, it's
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  about meticulous attention to really three critical
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  dimensionless numbers. We've got N Theta 95 for
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  blending, but remember you have to design for that dead zone
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  behind the baffle. Yep.
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  Then we have NJS for solids. Seeing how much something as
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  simple as a dish bottom can help.
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  And finally, the big one for reactions.
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  The damn killer number. It shows that scale up is all
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  about controlling that local energy dissipation epsilon to
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  manage what's happening at the molecular scale.
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  Right, it's about micro mixing. What's really striking is how
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  often the solution comes down to optimizing the flow in one tiny
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  specific region of the tank, not just the big picture average.
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  That's the core of it. Knowing where you're mixing time
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  is competitive with your reaction time.
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  That is the shortcut to avoiding incredibly expensive scale up
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  failures. You just you can't cheat that
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  ratio of Tau M over Tau R. That makes perfect sense and
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  that brings us to our final provocative thought for you to
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  think about. The sources mentioned that even
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  now with all our computing power, high fidelity
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  simulations, CFD, they still struggle.
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  They struggle to accurately predict critical things in these
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  multi phase systems like bubble sizes or that all important
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  local turbulence epsilon. So here's the question if
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  predicting something like the mass transfer coefficient KLA is
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  absolutely essential for scaling up these fast, complex
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  reactions, and our best simulations still can't reliably
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  model it, how much longer will expensive physical pilot testing
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  remain functionally irreplaceable for guaranteeing
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  yield and safety? Is the pilot plan on its way
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  out, or is it just waiting for a true quantum leap?
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  And how we model turbulence.