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Material Cycles and Energy Hierarchy. Calculating specific emergy of materials. Material Cycles and Energy Hierarchy. When self organization converges and concentrates high quality energy in centers, materials are also concentrated by the production functions.

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Material Cycles and Energy Hierarchy

Calculating specific emergy of materials


Material Cycles and Energy Hierarchy...

When self organization converges and concentrates high quality energy in centers, materials are also concentrated by the production functions.

Because available energy has to be used up to concentrate materials, the quantity of material flow also has to decrease in each successive step in a series of energy transformations.


Consumption of available energy is necessary to increase material concentration

(a) Concentration of materials indicated by density of dots;

(b) use of available energy to increase concentration and energy storage;

(c) emergy per mass increases with concentration;

(d) autocatalytic production process utilizing available energy to concentrate dispersed materials.

Dotted lines = energy flow only; solid lines = material flow.


Coupling of a trace material to energy flow and transformations...showing two stages.

On the left there is non-specific transport of trace concentrations by a carrier material. On the right there is a specific use of the trace material in an autocatalytic production process that accelerates energy use and material concentration.


Spatial convergence of materials to centers because of their coupling to the convergence of energy.

(a) Materials and energy transformation hierarchy on an energy systems diagram;

(b) spatial pattern of material circulation.


Inverse relation of material flow and emergy per mass.

(a) Inverse plot of rate of material concentration and emergy per mass where emergy flow is constant;

(b) systems diagram of the circulation of material (dark shading driven by a flow of empower Jemp;

(c) rate of materials concentration as a function of emergy per mass on double logarithmic coordinates.


Material Cycles and Energy Hierarchy...

The coupling of biogeochemical cycles to the energy transformation hierarchy explains the skewed distribution of materials with concentration.


Energy hierarchy concepts

(a) Web of energy transformation processes (rectangles) arranged in series with energy decreasing from left to right;

(b) energy system diagram of energy webs aggregated into a linear chain.

(c) energy spectrum: energy flow plotted as a function of transformity on logarithmic scales increasing from left to right

(d) sizes of unit centers and territories increasing with scale from left to right;

(e) periods and intensities of energy accumulation, pulsing, and turnover time increasing from left to right.


Distribution of materials in the biosphere follows a log normal distribution

Example: Distribution of lead in granites as a function of concentrations from Ahrens (1954). (a) Linear plot; (b) log normal plot.


Zones of material cycles in the hierarchical energy spectrum.

  • (a)Energy hierarchical spectrum showing the cycles of different materials in different zones;
  • (b) log-log plot of mass flow as a function of emergy per mass.

The principle of universal material distribution and processing was proposed by H.T. Odum as a 6th energy law.

      • “Materials of biogeochemical cycles are hierarchically organized because of the necessary coupling of matter to the universal energy transformation hierarchy.”

Material Cycles and Emergy

Two approaches for calculating Specific Emergy of elements based on abundance


Material Cycles and Emergy

Crustal Abundance of Elements


Material Cycles and Emergy

Reserves verses Crustal Abundance


Material Cycles and Emergy

A Global Enrichment Hierarchy

Background Concentration= 0.003%


Material Cycles and Emergy

Emergy Evaluation of Metals and Minerals

Generally to determine the emergy required to make something, we would evaluate the process, summing all the input energies….

However, the enrichment process for metals and minerals is most complex….


Material Cycles and Emergy

Enrichment Processes

  • hydrothermal processes: hydrothermal circulation cells, important factors = rock chemistry, water chemistry, P and T conditions, flux and time.
  • sedimentary sorting and placer deposits: panning for gold as one example.
  • intense chemical weathering: aluminum as an important example.
  • magmatic differentiation: e.g. the Bushveld complex in S. Africa.
  • many others processes. This forms the basis for the classification of types of ore deposits.

Material Cycles and Emergy

An Inferential Approach

  • Each element, at its background crustal concentration, is part of the global earth cycle
  • Elements at higher than their average crustal concentration represent bio/geo/hydro/chemical work.
  • The transformity scales linearly with enrichment factor (a hypothesis?)

Material Cycles and Emergy

Minimum % wt for metals to be mined profitably


Material Cycles and Emergy

Material Cycle of Lead ~ Specific Emergy of Ore Body


Material Cycles and Emergy

Specific emergy of metals based on crustal abundance and enrichment factor…


Material Cycles and Emergy

A second approach somewhat related….


Material Cycles and Emergy

Energy costs of mining & refining


Material Cycles and Emergy

Energy costs of mining & refining


Material Cycles and Emergy

Price is somewhat proportional to consumption


Material Cycles and Emergy

Global reserves of important metals…


Material Cycles and Emergy

Crustal abundance, ore cutoff factor, and price/ton


Material Cycles and Emergy

Estimating Ore Grade Cut-Off

  • Cutoff Concentration not available for all mined materials
  • Data readily available
    • Crustal abundance
    • Price per ton
  • So… develop an empirical relationship between Cutoff Concentration and abundance/Price.

Log(Cutoff Conc) = f(Abundance, Price)


Material Cycles and Emergy

Ln(Conc) = a + b1*Ln(Abundance)+b2*Ln(Price)


a = 2.9, b1 = -0.50, b2 = -0.18, b3 = 0.045


Material Cycles and Emergy

Predicted Specific Emergy of Elements

Two Different Earth Cycle Baselines (1.69E9, 1.4E8 sej/g)


Material Cycles and Emergy

Using 1.68E9 sej/g Earth Cycle Baseline