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Commerce · IV.02 · MMXXVI · daylight

La Bourse  /  Volume IV  /  Nº IV.02  /  Ten concept briefs

TEN CONCEPT BRIEFS · Chapter IV.02 — Materials and the Return Loop

One page each. A reader who reads only these ten pages has the chapter.

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BRIEF 1 — The Circularity Metric, and What Its Denominator Contains

The idea. The famous figure — the world is about seven percent circular — is one ratio with one definition: cycled material divided by total material input.

        cycled                8.4 Gt
  ---------------------  =  ----------  =  9.05 %      (2015 data)
   virgin  +  cycled        84.4 + 8.4

The denominator is everything that enters the economy, including fifteen-odd gigatonnes of fossil fuel that is burned, around thirty gigatonnes a year that goes into buildings and stays there for fifty years, and biomass that is eaten. None of that can come back this year, and some of it should not.

Worked example. Take the world material account for 2005: 62.0 Gt processed, 37 percent added to in-use stock (22.9 Gt), 44 percent dissipated or burned (27.3 Gt). What is physically available to return in the period is 62.0 − 22.9 − 27.3 = 11.8 Gt, and 4.0 Gt of it was recycled. As a share of input that is 6.5 percent. As a share of the returnable it is 34 percent.

Why it matters. Both numbers are true and they answer different questions. The first measures throughput. The second measures the recycling system. Quoting the first as a score for the second is the most common misreading in circular economy discussion, and it makes a functioning industry look like a failure.

You already know this because you have seen a conversion rate look terrible because somebody put every visitor in the denominator, including the ones who were never going to buy anything.

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BRIEF 2 — Recovery Rate and Process Yield Are Two Different Numbers

The idea. Two fractions sit between a product's death and a saleable material, and quoting one as if it were both is how recycling statistics flatter themselves.

• ρc, the end-of-life recovery rate — what fraction comes back at all.
• Y, the process yield — what fraction of what came back survives sorting, washing, melting and refining into something a buyer will accept.

Their product, ρ = ρc · Y, is what actually reaches the market.

Worked example. PET: 58 percent collected, 72 percent yield from bale to food-grade flake once labels, caps, fines and off-colour are removed. ρ = 0.58 × 0.72 = 0.418. Only forty-two percent of the PET put on the market returns to it, even though the collection headline says fifty-eight.

The trap inside the trap. Most published recycling rates also include new scrap — off-cuts and trimmings that never left the factory and were never at risk. That is good housekeeping, not recycling. Copper's quoted 32 percent "recycling input rate" becomes about 17 percent when only post-consumer metal is counted.

Why it matters. Every commercial decision in this field is priced off ρ, not off ρc. A plant sized on the collection rate is oversized by the yield.

You already know this because you have watched a pipeline report leads and a finance report revenue, and known that the ratio between them is where the business actually is.

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BRIEF 3 — The Secondary Supply Ceiling

The idea. Material reaching end of life this year entered service L years ago, when demand was smaller. So returns are always a fraction of a past, smaller economy — and that alone sets a ceiling.

                ρ
      c  =  -----------          ρ = ρc · Y      g = growth rate
             (1 + g)^L           L = mean product life

Worked example. Aluminium: ρc = 0.70, Y = 0.93, so ρ = 0.651. Mean product life twenty years, demand growth three percent. 1.03^20 = 1.806, so c = 0.651 / 1.806 = 36.0 percent. The observed global recycled content of aluminium is about 34 percent. A two-term formula, fed published inputs, lands two points off an independently measured industry.

Run for all five and the gaps are +2.0 (aluminium), +5.0 (steel), −1.8 (copper), +13.2 (PET), −2.8 (paper) percentage points.

Why it matters. It converts "we should recycle more" into a number with four named inputs, three of which are already in your systems. And it tells you the ceiling before you spend anything.

You already know this because you have tried to staff a team from internal promotion during a hiring boom, and found that the people available to promote were hired when the company was half the size.

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BRIEF 4 — The Steady-State Stock

The idea. In-use stock is the last L years of inflow. If inflow compounds at g, integrate it:

        K  =  D · (1 − e^(−gL)) / g            K/D → L  as  g → 0

K/D is "years of current demand held in service", and it is the single most useful description of a material system, because it tells you how big the mine above ground is relative to the one below.

Worked example. World crude steel 2008: D = 1.33 Gt/yr, L = 40 yr. At g = 2%: K/D = 27.53 yr, so K = 36.6 Gt. At g = 4%: K/D = 19.95 yr, so K = 26.5 Gt. Pauliuk, Wang and Müller measured the global in-use iron stock at about 25 Gt. Four percent is close to the actual compound growth of world steel over the prior four decades, and at that rate the formula is six percent off a measurement made by an entirely different method.

The figure to carry. Thirty-three gigatonnes of in-use steel at 20 MJ/kg is 660 EJ of embodied energy — about one full year of all human primary energy, standing up in buildings that already exist.

Why it matters. Faster growth makes a stock younger, so less of it has reached end of life, so less is available to recycle. Stock is a statement about growth history.

You already know this because a company that has doubled headcount in three years has almost nobody with five years' tenure, and everyone knows what that does to the culture.

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BRIEF 5 — The Growth Ceiling

The idea. Invert the supply ceiling and solve for growth. For a target secondary share c:

      g*  =  (ρ / c)^(1/L)  −  1

This is the fastest a material system can grow and still reach that share of supply from its own returns.

Worked example.

  steel   to 50 % secondary   (0.816/0.50)^(1/40) − 1  =  1.23 % / yr
  steel   to 70 % secondary   (0.816/0.70)^(1/40) − 1  =  0.38 % / yr
  alum.   to 50 % secondary   (0.651/0.50)^(1/20) − 1  =  1.33 % / yr
  copper  to 40 % secondary   (0.428/0.40)^(1/35) − 1  =  0.19 % / yr

And the cut. Set ρ = 1.00 — a perfect recycler, every atom returned. At two percent growth and a forty-year life, c = 1/1.02^40 = 45.3 percent. A flawless system still mines fifty-five percent of its demand.

Why it matters. The binding constraint on circularity is growth, not recovery. And because L sits in the exponent, doubling product life moves the ceiling further than any recovery-rate programme yet built.

You already know this because you cannot fill a growing team from its own alumni, however good your rehiring is.

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BRIEF 6 — The Entropy of Mixing Is Not the Problem

The idea. The usual explanation for downcycling is that mixing raises entropy and unmixing is thermodynamically expensive. Compute it and that explanation fails.

  ΔS_mix  =  −R [ x ln x + (1−x) ln(1−x) ]        W_min  =  T · ΔS

Worked example. Copper in shredded end-of-life vehicle steel at 0.35 wt%, a mole fraction of 0.003077. ΔS = 0.1735 J/mol·K. W = 298.15 × 0.1735 = 51.7 J/mol. There are 1000/55.85 = 17.91 moles of alloy per kilogram, so:

  minimum separation work           926 J/kg   =   0.93 kJ/kg steel
  making that steel from ore                      20,000 kJ/kg
  the thermodynamic floor is                          0.0046 %

Even at a second-law efficiency of one percent — dismal — separation costs 0.46 percent of what the steel cost to make.

So why does nobody do it? Because copper substitutes for iron on the lattice. It is in solid solution. There is no interface — no boundary, no surface, no second phase — for any separation process to grip. The barrier is structural, not thermodynamic.

Why it matters. "Physics forbids it" and "no process exists yet" are completely different claims with completely different budgets. This one is the second.

You already know this because the reason you cannot un-blend a cup of coffee is not that the universe charges too much. It is that nobody has built the strainer.

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BRIEF 7 — The Blending Inequality

The idea. For any element that cannot be removed, a melt is the mass-weighted mean of its inputs. So the blend can never be cleaner than its cleanest input, and a tight specification can only be met by dilution.

  f  =  (C_scrap − C_spec) / (C_spec − C_clean)     parts clean per part scrap

Worked example. Shredded end-of-life vehicle steel assays 0.35 % copper. Clean iron assays 0.01 %.

  automotive deep-drawing sheet  0.06 % Cu   (0.35−0.06)/(0.06−0.01)  =  5.80
  flat product, general          0.10 % Cu   (0.35−0.10)/(0.10−0.01)  =  2.78
  structural section             0.25 % Cu   (0.35−0.25)/(0.25−0.01)  =  0.42
  reinforcing bar                0.40 % Cu    no dilution needed

To put that scrap into car body sheet you must add 5.80 kilograms of clean iron per kilogram of scrap — and clean iron is exactly what you were avoiding making. So it goes to rebar. That is downcycling, and it is arithmetic.

Aluminium, same shape. A mixed wrought stream at 0.6 % silicon cannot be lifted to the 7.5–9.5 % that cast A380 requires by any amount of sorting — a thirteen-fold gap. It can only be alloyed upward, so wrought flows to cast, one way, into a sink that shrinks as engine blocks leave the fleet.

You already know this because you cannot raise a team's average by hiring more average people, and one bad input in a blend is never diluted away by enthusiasm.

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BRIEF 8 — A Waste Stream Is an Ore, and It Competes at Its Grade

The idea. Primary production is not expensive because ore is dirty. It is cheap per tonne of rock and expensive per tonne of metal. Compare a scrap stream to an ore on the same basis and a threshold grade appears.

      x*  =  E_feed / E_primary

where E_feed is processing energy per kilogram of feed and E_primary is energy per kilogram of finished metal.

Worked example. Primary copper from a 0.5 percent sulphide ore is 45 MJ per kilogram of metal, which is only 45 × 0.005 = 0.225 MJ per kilogram of rock — flotation is cheap per tonne. A mixed metallic residue must be smelted at roughly 3 MJ per kilogram of feed.

  x*  =  3.0 / 45.0  =  6.67 % copper

Automotive shredder residue assays one to two percent. It is three to seven times below the line. That is why it is landfilled by people who are not being careless.

The lever. Halve the feed processing energy and the threshold halves: 1.0 MJ/kg of feed gives x* = 2.22 %. The lever is physical pre-concentration, not a better smelter.

You already know this because you have decided not to chase a small account: not because the revenue was zero, but because the cost of serving it per pound of revenue was worse than the alternative use of the same hour.

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BRIEF 9 — The Yield Threshold, and Where Recovery Loses

The idea. Recovery costs energy per kilogram of input; you sell per kilogram of usable output. Yield converts one to the other, so recovery loses to primary production below a threshold yield:

      E_sec / Y  >  E_prim        i.e.        Y  <  Y*  =  E_sec / E_prim

Worked example, megajoules per kilogram.

The one to remember. Chemical depolymerisation of PET crosses at 66 percent monomer yield, and coloured, multilayer and thermoform streams routinely run below it. The technology works. On a contaminated feed it can cost more energy than making virgin PET out of oil.

And the counter-intuitive one. Recycled paper buys more purchased fossil energy than virgin kraft at any yield, because a kraft mill burns its own lignin and exports power while a deinking mill buys everything. Recycled paper still wins on fibre, land and water — but not automatically on purchased energy.

You already know this because a job with high rework is not cheaper than doing it right the first time, however low the hourly rate.

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BRIEF 10 — Technical and Biological Cycles, on the Evidence

The idea. Cradle to Cradle asks that every material be designed to stay in one of two cycles — technical (durable materials circulating among industries) or biological (materials that safely return to soil) — rather than being downgraded through both.

What the evidence says about the technical cycle: it works. Shaw's EcoWorx carpet tile, launched 1999, was designed so backing separates from face fibre; twenty-five years later it is still recovered at industrial scale. Interface's ReEntry is the same. The framework's chemical-inventory discipline — a banned list and a positive assessment of every input — has measurably changed formulations across furniture, textiles and flooring.

What the evidence says about the biological cycle: chemistry was never the constraint. A certified compostable package in a country where about 12 percent of households have food-waste collection is, for the other 88 percent, ordinary landfill with a certificate, and most industrial composters reject compostable packaging because they cannot identify it at the tipping face.

The scale check. Of 8,300 Mt of plastics made to 2015: 747 Mt recycled, 996 Mt incinerated, 6,557 Mt still in landfill or the environment.

The framework's real weakness, as Bjørn and Hauschild argued, is that it is relative rather than absolute — it says make materials that can cycle, and says nothing about how much throughput the system can carry. Read it with Brief 3 in hand and that gap closes.

You already know this because a product that can be returned is not the same as a product that is returned, and the difference is a logistics budget.