Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Energy Hierarchy Calculating specific emergy of materials

Emergy & Complex Systems Day 2, Lecture 3a…. 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. Material Cycles and Energy Hierarchy...

Emergy & Complex Systems Day 2, Lecture 3a…. (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. Consumption of available energy is necessary to increase material concentration

Emergy & Complex Systems Day 2, Lecture 3a…. 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. Coupling of a trace material to energy flow and transformations...showing two stages.

Emergy & Complex Systems Day 2, Lecture 3a…. (a) Materials and energy transformation hierarchy on an energy systems diagram; (b) spatial pattern of material circulation. Spatial convergence of materials to centers because of their coupling to the convergence of energy.

Emergy & Complex Systems Day 2, Lecture 3a…. (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 J emp ; (c) rate of materials concentration as a function of emergy per mass on double logarithmic coordinates. Inverse relation of material flow and emergy per mass.

Emergy & Complex Systems Day 2, Lecture 3a…. The coupling of biogeochemical cycles to the energy transformation hierarchy explains the skewed distribution of materials with concentration. Material Cycles and Energy Hierarchy...

Emergy & Complex Systems Day 2, Lecture 3a…. (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. Energy hierarchy concepts

Emergy & Complex Systems Day 2, Lecture 3a…. Example: Distribution of lead in granites as a function of concentrations from Ahrens (1954). (a) Linear plot; (b) log normal plot. Distribution of materials in the biosphere follows a log normal distribution

Emergy & Complex Systems Day 2, Lecture 3a…. (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. Zones of material cycles in the hierarchical energy spectrum.

Emergy & Complex Systems Day 2, Lecture 3a…. 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.”

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Two approaches for calculating Specific Emergy of elements based on abundance

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Crustal Abundance of Elements

Emergy & Complex Systems Day 2, Lecture 3a…. Reserves verses Crustal Abundance Material Cycles and Emergy

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy A Global Enrichment Hierarchy Background Concentration= 0.003%

Emergy & Complex Systems Day 2, Lecture 3a…. 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…. Emergy Evaluation of Metals and Minerals Material Cycles and Emergy

Emergy & Complex Systems Day 2, Lecture 3a….  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 Enrichment Processes

Emergy & Complex Systems Day 2, Lecture 3a….  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 An Inferential Approach

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Minimum % wt for metals to be mined profitably

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Material Cycle of Lead ~ Specific Emergy of Ore Body

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Specific emergy of metals based on crustal abundance and enrichment factor…

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy A second approach somewhat related….

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Energy costs of mining & refining

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Energy costs of mining & refining

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Price is somewhat proportional to consumption

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Global reserves of important metals…

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Crustal abundance, ore cutoff factor, and price/ton

Emergy & Complex Systems Day 2, Lecture 3a….  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 Estimating Ore Grade Cut-Off

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Ln(Conc) = a + b 1 *Ln(Abundance)+b 2 *Ln(Price) +b 3 *Ln(Abundance)*Ln(Price) a = 2.9, b 1 = -0.50, b 2 = -0.18, b 3 = Ln(Conc) = a + b 1 *Ln(Abundance)+b 2 *Ln(Price) +b 3 *Ln(Abundance)*Ln(Price) a = 2.9, b 1 = -0.50, b 2 = -0.18, b 3 = 0.045

Emergy & Complex Systems Day 2, Lecture 3a…. Material Cycles and Emergy Predicted Specific Emergy of Elements Two Different Earth Cycle Baselines (1.69E9, 1.4E8 sej/g)

Emergy & Complex Systems Day 2, Lecture 3a…. Using 1.68E9 sej/g Earth Cycle Baseline Material Cycles and Emergy