emergy & complex systems day 2, lecture 3a…. material cycles and energy hierarchy calculating...

Emergy & Complex Systems

Day 2, Lecture 3a….

Material Cycles and Energy Hierarchy

Material Cycles and Energy Hierarchy

Calculating specific emergy of materials



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...



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



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.



(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.


Day 2, Lecture 3a…. .

Emergy per Mass Em, emjoules/kilogram

Line of Contant Empower Jemp

1.0

0Log 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.



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

Material Cycles and Energy Hierarchy...



.

Feedback Control Loops

104 103

103 102 10

10105

104

106

Degraded Energy

1021

(a)

(b)

Transformity

10 102 103 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


Day 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


Day 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.



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 EmergyMaterial Cycles and Emergy

Two approaches for calculating Specific Emergy of elements based on abundance




Crustal Abundance of Elements

Crustal Abundance of Elements



Reserves verses Crustal Abundance

Reserves verses Crustal Abundance





A Global Enrichment Hierarchy

A Global Enrichment Hierarchy

Background Concentration= 0.003%



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




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.


Enrichment Processes



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?)


An Inferential Approach




Element

% of crust by

wieght

Minimum %

profitably

extracted

Enrichment

Factor

Aluminum 8.070% 30.00% 3.7

Iron 5.050% 30.00% 5.9

Titanium 0.620% 40.30% 65.0

Phosphorus* 0.130% 30.00% 230.8

Manganses 0.090% 35.00% 388.9

Chromium 0.035% 30.00% 857.1

Nickel 0.019% 1.50% 78.9

Copper 0.0068% 1.00% 147.1

Lead 0.0010% 0.04% 40.0

Uranium 0.00018% 0.01% 55.6

Silver 0.000008% 0.008% 1000.0

Mercury 0.0000067% 0.17% 25000.0

Gold 0.00000031% 0.0014% 4500.0

* estimate

Element

% of crust by

wieght

Minimum %

profitably

extracted

Enrichment

Factor

Aluminum 8.070% 30.00% 3.7

Iron 5.050% 30.00% 5.9

Titanium 0.620% 40.30% 65.0

Phosphorus* 0.130% 30.00% 230.8

Manganses 0.090% 35.00% 388.9

Chromium 0.035% 30.00% 857.1

Nickel 0.019% 1.50% 78.9

Copper 0.0068% 1.00% 147.1

Lead 0.0010% 0.04% 40.0

Uranium 0.00018% 0.01% 55.6

Silver 0.000008% 0.008% 1000.0

Mercury 0.0000067% 0.17% 25000.0

Gold 0.00000031% 0.0014% 4500.0

* estimate

Minimum % wt for metals to be mined profitably

Minimum % wt for metals to be mined profitably




Material Cycle of Lead ~ Specific Emergy of Ore Body

Material Cycle of Lead ~ Specific Emergy of Ore Body



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+08

Silicon 27.690% 7.81E+24

Aluminum 8.070% 2.28E+24 30.00% 5.22E+08

Iron 5.050% 1.42E+24 30.00% 8.34E+08

Calcium 3.650% 1.03E+24

Sodium 2.750% 7.76E+23

Potassium 2.580% 7.28E+23

Magnesium 2.080% 5.87E+23

Titanium 0.620% 1.75E+23 40.30% 9.12E+09

Phosphorus 0.130% 3.67E+22

Manganses 0.090% 2.54E+22 35.00% 5.46E+10

Sulfer 0.052% 1.47E+22

Barium 0.050% 1.41E+22

Chlorine 0.045% 1.27E+22

Chromium 0.035% 9.87E+21 30.00% 1.20E+11

Flourine 0.029% 8.18E+21

Zirconium 0.025% 7.05E+21

Nickel 0.019% 5.36E+21 1.50% 1.11E+10

copper 0.0068% 1.92E+21 1.00% 2.06E+10

lead 0.0010% 2.82E+20 0.04% 5.61E+09

uranium 0.00018% 5.08E+19 0.01% 7.80E+09

silver 0.000008% 2.26E+18 0.00008 1.40E+11

mercury 0.0000067% 1.89E+18 0.001675 3.51E+12

Gold 0.00000031% 8.74E+16 0.00001395 6.32E+11

Weight of crust:

Contienetal 2.23E+22Kg

Oceanic 5.90E+21kg

2.82E+25g

Annual emergy 1.58E+25sej

crust turnover time 2.50E+08yrs

total 3.96E+33

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+08

Silicon 27.690% 7.81E+24

Aluminum 8.070% 2.28E+24 30.00% 5.22E+08

Iron 5.050% 1.42E+24 30.00% 8.34E+08

Calcium 3.650% 1.03E+24

Sodium 2.750% 7.76E+23

Potassium 2.580% 7.28E+23

Magnesium 2.080% 5.87E+23

Titanium 0.620% 1.75E+23 40.30% 9.12E+09

Phosphorus 0.130% 3.67E+22

Manganses 0.090% 2.54E+22 35.00% 5.46E+10

Sulfer 0.052% 1.47E+22

Barium 0.050% 1.41E+22

Chlorine 0.045% 1.27E+22

Chromium 0.035% 9.87E+21 30.00% 1.20E+11

Flourine 0.029% 8.18E+21

Zirconium 0.025% 7.05E+21

Nickel 0.019% 5.36E+21 1.50% 1.11E+10

copper 0.0068% 1.92E+21 1.00% 2.06E+10

lead 0.0010% 2.82E+20 0.04% 5.61E+09

uranium 0.00018% 5.08E+19 0.01% 7.80E+09

silver 0.000008% 2.26E+18 0.00008 1.40E+11

mercury 0.0000067% 1.89E+18 0.001675 3.51E+12

Gold 0.00000031% 8.74E+16 0.00001395 6.32E+11

Weight of crust:

Contienetal 2.23E+22Kg

Oceanic 5.90E+21kg

2.82E+25g

Annual emergy 1.58E+25sej

crust turnover time 2.50E+08yrs

total 3.96E+33


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




A second approach somewhat related….




Energy costs of mining & refining

Energy costs of mining & refining




Price is somewhat

proportional to

consumption

Price is somewhat

proportional to

consumption




Global reserves of important metals…

Global reserves of important metals…




Crustal abundanc

e, ore cutoff

factor, and price/ton

Crustal abundanc

e, ore cutoff

factor, and price/ton



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)


Estimating Ore Grade Cut-Off




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

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




Predicted Specific Emergy of Elements

Predicted Specific Emergy of Elements

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



Using 1.68E9 sej/g Earth Cycle Baseline


emergy & complex systems day 2, lecture 3a…. material cycles and energy hierarchy calculating...

Documents

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