1

Materials & ResourcesSankey Diagrams

Scott Matthews12-712 / 19-622

Administrative Issues

HW 4 Due Today No HW due next week (taking a week off)

Project Updates Any left?

HW 5 coming Start tracking your expenses AND your

general “material/resource” flow starting tomorrow am. Will need to for next HW.

2

Mass Balance

Fundamental principle of engineering / environmental engineering (law of conservation of mass)

Commoner: “everything must go somewhere”

Physical quantitiesEnergyCalories, etc.

Relevant: stocks and flows, ins and outs

3

Basic Plan for an MFA

Begin building a simple IN=OUT modelStart assembling IN, OUT flow data

Are there many more relevant IN, OUT flows?Is there a substantial stock or sink?

Do we have sufficient data to quantify them?Continue iterating as data and time allowWhen done, summarize as many disaggregate

stocks and flows as possible Typically express results “over life cycle”

4

5Source: USGS, Obsolete Computers, “Gold Mine,” or High-Tech Trash? Resource Recovery from Recycling

Our Computer “MFA”

6

http://gdi.ce.cmu.edu/comprec/NEWREPORT.PDF

7

1991 Study 1997 Study

Computer Flow Study Results1991 Model:

By 2005 - 340 million sold, 150 million landfilled

1997 Model: By 2005 – 680 million sold, 55 million landfilled (one acre

piled 4000 feet high) 150 million recycled (originally almost none)

What affects them? Shouldn’t percents/etc change year by year (ie by an increasing or decreasing trend of % recycled?)

8

Policy Relevance of MFA

Can we track natural versus anthropogenic flows? JIE paper – Cadmium – only way to reduce is to

eliminate inflow But inflow is byproduct of Zinc; either need to

eliminate zinc production or cut off co-product Structure of such studies – and construction of the

stock/flow models – yields insightsCan we learn more about connections

between stocks and flows, our activities?

9

MFA Issues

Data / methods are largest barriers (conceptually simple otherwise)

What about uncertainty?

10

Sankey Diagrams

Generally used for Energy flow analyses

Implicit assumptions The diagrams concern quantity sizes that are related to

a period in time or to a functional unit, such as a product unit.

The quantity scale is proportional (i.e., twice the quantity is represented by an arrow that is twice as wide).

Inventories are not taken into account (i.e., there is no stock formation).

An energy or mass balance is maintained.

11

12

13Source: WRI, http://www.wri.org/image/view/9529/_original

14

Lead Flows 1970 (USGS)

15

Lead Flows 1993

16

Non-renewable resource consumption

As new resources identified, production and consumption small, grow slowly With new uses, new demand, thus

explorationDemand continues as we find new supply

New supplies become harder to findInevitably raises costs, reduces demand

Feedback loop to looking for less supply Eventually “known” reserves run out

17

Hubbert’s Curve (Shell Oil 1950s)

Projects rate of oil production over timeBased on peak of oil well discovery in 1948,

Hubbert in 1956 accurately predicted that oil production in the contiguous United States would peak around 1970. Since applied to global oil production

Implication: a steep drop in production implies global oil production will decline so rapidly we will not have enough time to develop alternatives

18

Source: http://en.wikipedia.org/wiki/Hubbert_curvehttp://www.hubbertpeak.com/hubbert/1956/1956.pdf (original 1956 report)

Hubbert’s assumptions

Production curve: We know production=0 at t=0, t=infinity If P=dQ/dt (change in production).. Area under curve = total production

Q(t) cumulative production

Hubbert inevitably assumes symmetric production functions

19

20

Source http://www.hubbertpeak.com/hubbert/1956/1956.pdf

Hubbert’s “prior data”

Production in “old” regions of the US

21

Any curve that starts and ends at zero, hits a peak, and has as the area the total available resource is possible The question is which is more likely?

22

In-Class Exercise: Hubbert curve for global oil (conventional only)

Find/draw a Hubbert curve.Simply put, relevant data to estimate ultimate

production are: U= cumulative production, reserves, “yet to find” “Yet to find” a “round off error” kind of number

representing oil we think is out there Sum of these 3 ~ ultimate production (U)

Saudi Arabia - #1 producer - notoriously quiet on publicly revealing their amount of reserves. Why?

23

Data Point #1

24

Data Points #2

25

Relevance for Other Materials

Fossil fuels, e.g. petroleum are primary needs in production of everything else Plastics – petrochemical feedstocks

(part of push for biobased feedstocks)

26