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Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Energy Hierarchy
Calculating specific emergy of materials
Emergy & Complex SystemsDay 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 SystemsDay 2, Lecture 3a….
Energy Concentration andEmergy per Unit Mass
Natural Depreciation(Second Law)
(a) Concentration Gradient
Materials
Energy Required(b) Process of Concentrating Materials
(c) Emergy per Mass
(d) Emergy and Materials into Production
Production Process
Energy & Emergy
Dispersed Material
Storages
Recycle
(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 SystemsDay 2, Lecture 3a….
Increasing Emergy/Mass
Trace Material Embedded in Carrier
Cycle of Carrier
Energy & Emergy
TraceMaterial atBackgroundConcentration
AutocatalyticProcessRequiringTrace Material
Trace Material:Carrier FluidEnergy Flow
DispersalRecycle
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 SystemsDay 2, Lecture 3a….
(b) Spatial Convergence of Materials
(a) Materials Combined with Energy Flows
EnergySources
Dispersed Materials
Recycle
= Energy= Materials
DispersedMaterials
CENTER =
(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 SystemsDay 2, Lecture 3a…. .
Emergy per Mass Em, emjoules/kilogram
Line of Contant Empower Jemp
1.0
0 Log Em
0
Line of ConstantEmpower Jemp
Log Jm = Log Jemp - Log Em
Jemp
Jm = Jemp/Em
Em = (Emergy/Mass)
Area Proportionalto Empower
Jemp
(a)
Emergy per gram
(emjoules/hectare)
Background Concentration
EmergySource
(b)
(c)
(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.
Inverse relation of material flow and emergy per mass.
Emergy & Complex SystemsDay 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 SystemsDay 2, Lecture 3a….
.
Feedback Control Loops
104 103
103 102 10
10105104
106
Degraded Energy
1021
(a)
(b)
Transformity10 102 103 1051041
1
(c)
Source
Increasing Unit Size and Size of Territory
Increasing Period and Pulse Amplitude
(d)
(e)
(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 SystemsDay 2, Lecture 3a….
.
Parts Per Million Lead0 50 80
15
10
5
5 ppm interval
0
Ahrens 1954
15
10
50-1.2 0.0 0.5 1.6 2.4 3.2
Log ppm Lead
Log Normal
(a) Lead Distribution in Granites
(b)
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 SystemsDay 2, Lecture 3a….
.
1 102 104 106 108
103
104
105
106
102
10
1
Vapor
RainRunoff
Glaciers
1010
Biogeochemical Cycles
(a) Material Spectrum
Log Emergy per Mass
Zone of moneyCirculation
(b) Examples
CarbonWater
LeavesTrunks
Photosyn.
107
Log Emergy per Mass, sej/g
(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 SystemsDay 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 SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Two approaches for calculating Specific Emergy of elements based on abundance
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Crustal Abundance of Elements
Emergy & Complex SystemsDay 2, Lecture 3a….
Reserves verses Crustal Abundance
Material Cycles and Emergy
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
A Global Enrichment Hierarchy
Background Concentration= 0.003%
Emergy & Complex SystemsDay 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 SystemsDay 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 SystemsDay 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 SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Element% of crust by
wieght
Minimum % profitably extracted
Enrichment Factor
Aluminum 8.070% 30.00% 3.7Iron 5.050% 30.00% 5.9
Titanium 0.620% 40.30% 65.0Phosphorus* 0.130% 30.00% 230.8Manganses 0.090% 35.00% 388.9Chromium 0.035% 30.00% 857.1
Nickel 0.019% 1.50% 78.9Copper 0.0068% 1.00% 147.1Lead 0.0010% 0.04% 40.0
Uranium 0.00018% 0.01% 55.6Silver 0.000008% 0.008% 1000.0
Mercury 0.0000067% 0.17% 25000.0Gold 0.00000031% 0.0014% 4500.0
* estimate
Minimum % wt for metals to be mined profitably
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Material Cycle of Lead ~ Specific Emergy of Ore Body
Emergy & Complex SystemsDay 2, Lecture 3a….
Specific emergy of minerals
Element% of crust by
wieght Weight (g)
Minimum % profitably extracted
Specific Emergy (sej/g)
Total Crust 100% 2.82E+25 1.40E+08Silicon 27.690% 7.81E+24
Aluminum 8.070% 2.28E+24 30.00% 5.22E+08Iron 5.050% 1.42E+24 30.00% 8.34E+08
Calcium 3.650% 1.03E+24Sodium 2.750% 7.76E+23
Potassium 2.580% 7.28E+23Magnesium 2.080% 5.87E+23Titanium 0.620% 1.75E+23 40.30% 9.12E+09
Phosphorus 0.130% 3.67E+22Manganses 0.090% 2.54E+22 35.00% 5.46E+10
Sulfer 0.052% 1.47E+22Barium 0.050% 1.41E+22Chlorine 0.045% 1.27E+22
Chromium 0.035% 9.87E+21 30.00% 1.20E+11Flourine 0.029% 8.18E+21
Zirconium 0.025% 7.05E+21Nickel 0.019% 5.36E+21 1.50% 1.11E+10copper 0.0068% 1.92E+21 1.00% 2.06E+10lead 0.0010% 2.82E+20 0.04% 5.61E+09
uranium 0.00018% 5.08E+19 0.01% 7.80E+09silver 0.000008% 2.26E+18 0.00008 1.40E+11
mercury 0.0000067% 1.89E+18 0.001675 3.51E+12Gold 0.00000031% 8.74E+16 0.00001395 6.32E+11
Weight of crust:Contienetal 2.23E+22KgOceanic 5.90E+21kg
2.82E+25g
Annual emergy 1.58E+25sejcrust turnover time 2.50E+08yrstotal 3.96E+33
Material Cycles and Emergy
Specific emergy of metals based on crustal abundance and enrichment factor…
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
A second approach somewhat related….
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Energy costs of mining & refining
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Energy costs of mining & refining
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Price is somewhat
proportional to
consumption
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Global reserves of important metals…
Emergy & Complex SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Crustal abundanc
e, ore cutoff
factor, and price/ton
Emergy & Complex SystemsDay 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 SystemsDay 2, Lecture 3a….
Material Cycles and Emergy
Ln(Conc) = a + b1*Ln(Abundance)+b2*Ln(Price)+b3*Ln(Abundance)*Ln(Price)
a = 2.9, b1 = -0.50, b2 = -0.18, b3 = 0.045
Emergy & Complex SystemsDay 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 SystemsDay 2, Lecture 3a….
Using 1.68E9 sej/g Earth Cycle Baseline
Material Cycles and Emergy