Reflux / syrup

Why corn syrup is in everything

Corn starch breaks down into glucose, and glucose is not sweet enough to sell. Fructose is. So a corn plant pours glucose through a packed column of tiny beads with an enzyme locked inside them, at about 55 degrees, and the enzyme flips glucose into fructose until the mix sits near 42 percent fructose. That is high-fructose corn syrup: cheaper than sugar, and it pours. US output went from 2.2 million tons a year in 1980 to 9.5 million in 1999. The interesting part is not the sugar. It is that the reactor you size on day one is a different reactor by month two, and most fourth-years size it as if it runs at its ceiling.

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01

Glucose is not sweet enough

Starch is a chain of glucose. Break the chain and you get glucose syrup, which is cheap, pours well and tastes thin. Measured against table sugar at 1.00, glucose comes in at 0.75. Fructose, the same atoms in a different arrangement, comes in at 1.73. So the whole industry turns on one question: can you rearrange one into the other cheaply enough to be worth it.

glucose 0.75 fructose 1.73 sweetness, table sugar = 1.00
Table sugar is 1.00. Glucose is 0.75, which is why a syrup made of it tastes thin, and fructose is 1.73. The plant is not making a new sugar, it is rearranging one it already has into the sweeter shape.

One enzyme, locked inside a bead

The answer is glucose isomerase. It is expensive, so nobody dissolves it in the syrup and throws it away: it is immobilised, locked inside porous carrier beads that stay in the column while the sugar flows past. The beads are packed into a steel column, the glucose goes in the top at about 55 degrees, and the enzyme flips glucose into fructose on the way down.

It stops near 42 percent fructose, and that is not a failure of the equipment. The reaction is an equilibrium, and at these temperatures it sits between 42 and 50 percent. A plant that wants more fructose than that does not run the column harder, it separates the product afterwards and blends it back.

glucose beads fructose 55 °C 42% fructose
The column in section: feed through a distributor, a packed bed of beads with the enzyme locked inside them, a support screen, and the product off the bottom. Glucose goes in at the top at about 55 degrees and leaves as a mixture sitting near 42 percent fructose. It is an equilibrium, not a conversion, so it stops there.

The rule most engineers get wrong

An enzyme has a fixed number of working slots. At low sugar most of them sit empty, so adding sugar genuinely adds speed. Past a certain point every slot is busy, the speed flattens, and pouring in more sugar does nothing at all. Double the enzyme and you double the ceiling, because the ceiling is just how many slots there are. Double the sugar and you get almost nothing.

enzyme sugar speed the ceiling
An enzyme has a fixed number of working slots. At low sugar most of them are empty, so more sugar means more speed. Once they are all busy the speed flattens and the extra sugar queues outside. Adding enzyme adds slots, which is why it lifts the ceiling and sugar cannot.
v = Vmax · S / (Km + S)   and   Vmax = kcat · [E] The ceiling is proportional to how much enzyme is present, so the enzyme term scales it one for one. The sugar term is a ratio that can never exceed 1, so no amount of sugar can push past the ceiling. Km is the sugar concentration that gets you to half of it.

Add sugar, or add enzyme

The plant sits at about 4 times Km. Try to beat the ceiling with sugar.

Speed0.80
Its own ceiling1.00
Fraction of the ceiling80%
Sugar is nearly spent

At four times Km the slots are already 80 percent busy. Doubling the sugar from here buys 11 percent. Doubling the enzyme buys 100 percent.

The bead is never at its ceiling

That is the textbook rule, and a packed bed breaks it immediately. The enzyme is not in the liquid, it is inside a bead, and the sugar has to diffuse in before it finds any. Sugar is consumed on the way, so the concentration falls from the rim toward the centre and the enzyme in the middle of the bead works in a thinner solution than the enzyme at the edge. The whole bead therefore runs below the rate its own kinetics promise, from the first hour of its life.

How far below is set by the bead radius against how fast the enzyme eats compared with how fast sugar can move, which is the Thiele modulus. Small beads are nearly fully used; large beads are mostly dead weight in the middle. Small beads also pack tighter and cost pressure drop, which is the trade.

the ceiling the bead
One bead, cut open. The sugar has to diffuse in before it meets an enzyme, so the inside of the bead runs at a lower concentration than the liquid around it, and the enzyme sitting in the middle does less work than the enzyme at the rim. The bead never reaches the rate its own kinetics promise.

How much of the bead is actually working

The effectiveness factor for a sphere, with the square root of k over the effective diffusivity taken as 20 per mm.

Thiele modulus2.67
Effectiveness0.33
Rate you actually get33%
Two thirds of the enzyme is idling

The sugar never reaches the middle of the bead in any strength, so the enzyme there is paid for and not used.

And the enzyme dies while you watch

Glucose isomerase is run hot because hot is fast, and hot is also what kills it. In one study it lost half its activity in 45 days at 60 degrees. Industrial columns are quoted with longer half-lives, but the shape does not change: it is a first-order decay and it never levels off.

So the operators do the only thing that holds the product spec. If the column has less activity in it, the syrup needs longer in the column to reach 42 percent, which means less flow. They turn the flow down a little, week after week, until the bed is swapped. The composition on the readout never moves. The throughput does, and that is what the decay actually costs.

0 45 90 days 45 days · 60 °C
The enzyme dies slowly. In one study it lost half its activity in 45 days at 60 degrees. Industrial columns are quoted with longer lives, but the shape is the same and it never flattens out.
42% fructose
What the operators actually do about it: turn the flow down a little, week after week, so the syrup keeps coming off at 42 percent. The readout holds steady and the throughput is what pays for it.

The turn-down, week by week

Holding the same conversion means holding the same contact time per unit of activity, so the flow you can run is proportional to the activity left.

Activity left50%
Flow you can run50%
Fructose off the bottom42%
Half the plant, same syrup

The spec is held by giving up throughput. Nothing on the product analyser moves, which is exactly why this is easy to miss when you size the thing.

Three layers, and a reactor that changes under you

Kinetics gives you a ceiling. Diffusion inside the bead says how far under that ceiling you actually sit. Decay says how fast that number moves. Size the column on the first one alone and you have sized it for a plant that has never existed, on its best day, which it does not have.

kinetics a diffusion penalty a decay clock
Kinetics gives the ceiling, diffusion says how far under it the bead sits, and decay says how fast that moves. A reactor sized on the first of those alone is sized for a plant that does not exist.

This is the layer I am building: the packed-bed model with the diffusion penalty and the decay clock in it, driving a real simulator rather than a spreadsheet.

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