The basic model for inventory analysis

Transcription

1 The bsic model for inventory nlysis Lecture Notes for ME515 Prepred by Joyce Smith Cooper Professor of Mechnicl Engineering University of Wshington See Chpter 2 of Heijungs nd Suh (22) The Computtionl Structure of LCA, Kluwer Acdemic Publishers.

2 Wht to include in your gol nd scope definition The structure of your gol nd scope report is described in the ISO Stndrds. define the gol of the study; define the (function), functionl unit, nd reference flows; define the initil system boundries (including process flow digrms depicting mjor mteril flows); describe the criteri for inclusion of inputs nd outputs describe the impct ssessment methodology describe the dt qulity requirements nd scoring method; nd mke recommendtions for criticl review. You must lso include brief description of the LCA methodology nd review of existing relted LCAs s my hve been included in your proposl. All cittions should be complete in APA formt

3 Exmple: Aluminum Plte Fbriction Buxite Mining Alumin Refining Anode Production Aluminum Smelting Ingot Csting Shpe Csting Stndrd Mchining Solvent Clening Anodizing Electricity Production Fuel Production

4 Exmple: Aluminum Plte Fbriction Note the rbitrry scles kg luminum L fuel kwh electricity kg - km trnsport kg luminum prt kg wste luminum L wter L wstewter Crbon dioxide Sulfur dioxide Buxite Residues Crude oil

5 The process vector The unit process luminum prt production cn be represented by the process vector p: kg luminum 1.5 kwh electricity.2 kg - km trnsport 15 p = kg luminum prt = 1 kg wste luminum.5 L wter.18 L wstewter.18

6 The process vector If we re interested in modeling prt, luminum, electricity, nd fuel production nd trnsport we need to dd inputs nd outputs to the bsis. For prt production, the process vector becomes: p pp kg luminum 1.5 L fuel kwh electricity.2 kg - km trnsport 15 kg luminum prt 1 kg wste luminum.5 = L wter =.18 L wstewter.18 Crbon dioxide Sulfur dioxide Buxite Residues Crude oil

7 The process mtrix And the system is represented by the process mtrix Prt production kg luminum 1.5 L fuel kwh electricity.2 kg - km trnsport 15 kg luminum prt 1 kg wste luminum.5 P = L wter =.18 L wstewter.18 Crbon dioxide Sulfur dioxide Buxite Residues Crude oil Al production 1 52,52 16,628 16,628 4,581 3,581 Elect. production Fuel production Trnsport.45 1,.12.15

8 Types of flow Note tht ISO 1441 refers to product nd elementry flows: Idelly, the product system should be modeled in such mnner tht inputs nd outputs t its boundries re elementry flows. Next we prtition the process mtrix into: Economic flows Flows within the economic system Environmentl flows (.k.. environmentl interventions or simply interventions ) Flows from nd into the environment Wter CO 2 Al production Prt production Trnsport Economic Flows Elect. production Fuel production Environmentl Flows

9 Types of flows

10 The technology nd intervention mtrices The prtitioned mtrix is: With A s the technology mtrix nd B s the intervention mtrix A P = B Prt production kg luminum 1.5 L fuel kwh electricity.2 kg - km trnsport 15 kg luminum prt 1 = kg wste luminum.5 P = L wter =.18 L wstewter.18 Crbon dioxide Sulfur dioxide Buxite Residues Crude oil Elect. production Al production , ,628 16, ,581 3,581 Fuel production Trnsport.45 1,.12.15

11 Where re we going? So now we hve prtitioned mtrix, representing the economic nd environmentl flows of our life cycle There re 5 processes in the system boundry We need to know how much of ech process is needed for the reference flows (wht is demnded from the system), Which is driven by the economic flows As=f How much of ech processis represented s scling vector s How much of ech economic flow we need for our reference flows is represented by the demnd vector f

12 Demnd vectors ccount for reference flows Suppose the functionl unit for the luminum plte is: to mintin certin deflection for given lod (i.e., certin stiffness) within certin design footprint nd ble to be used in slightly corrosive environment The relted reference flow is ccomplished by 1 kg luminum prt The demnd vector f represents the set of economic flows tht correspond to the reference flow

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14 The inventory problem nd its solution Before scling, the unit processes produce 1 kg luminum prt 1 kg luminum 1 kwh electricity 1 L fuel 1, kg-km trnsport Need to solve for system tht meets the demnd To ccomplish this, we need the scling vector s s = s s s s s

15 The inventory problem nd its solution The scling vector reltes the technology mtrix to the demnd vector or As=f s s s s s See eq nd = f f f f f

16 The inventory problem nd its solution Given tht the technology mtrix A is known nd tht the finl demnd vector f is known, the scling vector cn be found from s=a -1 f (eq. 2-21) To solve the inventory problem, we still need to find the vlues of the system-wide ggregted environmentl flows for the g vector

17 So, this is the result s tells metht in the production 1 kg prt, I need.16 x 1L of fuel g tells me tht when I consider ech element of s nd the CO2 emissions from the corresponding unit processes, my system will emit totl of 9.5 kg CO2

18 Using MSExcelmtrix functions MA MANY students prefer to use MATLAB (nd there is code in the bck of the text). I like Excel becuse I cn build prmetric models to feed into ech cell of the A nd B mtrices or the f vector(s). If you decide to go with MATLAB, be sure to djust the code so you (nd I) cn look t s. This ends up being VERY helpful in finding errors in your mtrices.

19 The inventory problem nd its solution The scling vector (from s=a -1 f ) provides direct clue to the finl step in solving the inventory problem. The scling of unit processes ffects both economic nd environmentl flows, nd its solution llows us to estimte the inventory vector g, which gives us the life cycle mounts of ech environmentl flow. g=bs (eq. 2.29) The vector g is the solution to the inventory problem And it cn be the mtrix G if you go with demnd mtrix F.

20 Generl formultion A process vector p represents the flow of goods, mterils, services, wstes, substnces, nturl resources, lnd occuption, sound wves, nd other relevnt items The bsic model ssumes tht industril ctivity cn be described with constnt technicl coefficients, i.e., representing liner technology in terms of production: s 1 p 1 +s 2 p 2 + =f such tht there re no scle effects in production or consumption!!!!! scling fctors hve no consistent dimension: you cn develop dt sets bsed on ny mount of production 1kWh electricity, 1kWh electricity, 3.14 kwh electricity

21 Notes on the bsic model The bsic model presents mtrix inversion s the mens to solve the system, which requires squre nd invertible/ non-singulr technology mtrix The inventory model is systemtic construction of set of liner blnce equtions, With one economic flow nd one scling fctor for ech unit process. A squre mtrix tht is not invertible is clled singulr or degenerte. A singulr mtrix hs determinnt of zero (so you wnt nonzero determinnt)

22 Singulrity in the technology mtrix A must be squre nd invertible/ non-singulr mtrix Consider singulr technology mtrix Suppose electricity production uses 2 L fuel to mke 1 kwh electricity Suppose fuel production produces 1 L fuel using 5 kwh electricity In this exmple, fuel production is multiple of electricity production (by fctor of -.5) which leds to singulrity of A. If these were our only choices, we wouldn t use fuel to mke electricity (unless we subsidize) fuel production electricity production fuel production A= -2 1 L fuel 1-5 kwh electricity det (A)= 2 L fuel there is no net product! electricity production 1 kwh

23 Notes on the bsic model Agin, this mens the bsic model only pplies when the number of processes equls the number of economic flows This is not utomticlly the cse in: Cut-off of economic flows Multifunctionl unit processes A choice between lterntive processes Closed look recycling Which re discussed in chpters 3 nd 4 of the text

24 Using full LCIs s unit processes The boundries of unit process re rbitrry so unit process cn represent full LCA So you could hve unit process nmed the life cycle of electricity We do this ALL the time It just mens tht insted of hving ll of the unit processes needed to mke electricity in your mtrix, you insted hve just one This is just leverging existing LCAs. For exmple, if you re interested in using the work of others in this clss, consider the following

25 Suppose this is Joyce s LCA And suppose this is your system Then your A nd B mtrices might look like this

26 Flexibility of the Bsic Inventory Model The bsic inventory model is VERY flexible Unitprocessscope (columns in A nd B) Anything from single ctivity to n entire life cycle f vector scope f cn represent single flow (e.g., 1 kg luminum prt, use of computer over 5-yers) f cn represent brekdown of mterils, energy use, lnd use. One size does not fit ll! Your inventory is YOUR MODEL Consider 2 inventory models for THE SAME computer. the life cycle of Pls c the life cycle of Aluminum the life cycle of Steel the life cycle of Copper the life cycle of Glss the life cycle of Pckging the life cycle of Component fb the life cycle of Computer ssembly the life cycle of Logis cs the life cycle of Retil the life cycle of Electricity the life cycle of Pckging disposl the life cycle of Metls recycling the life cycle of Pls c nd glss to wste mngement

27 Flexibility of the Bsic Inventory Model the life cycle of Pls c the life cycle of Aluminum the life cycle of Steel the life cycle of Copper the life cycle of Glss the life cycle of Pckging the life cycle of Component fb the life cycle of Computer ssembly the life cycle of Logis cs the life cycle of Retil the life cycle of Electricity the life cycle of Pckging disposl the life cycle of Metls recycling the life cycle of Pls c nd glss to wste mngement VERSION 1 of the LCA for computer.

28 Version 1: A is 21x21 f is 1 & zeros Gives mtching scling fctors Version 2: A is 2x2 f is #s & zeros

29 Version 1: A is 21x21 f is 1 & zeros Gives mtching scling fctors Version 2: A is 2x2 f is #s & zeros

30 Summry As=f, s=a -1 f, ndg=bs OR AS=F, S=A -1 F, ndg=bs A must be squre nd invertible/ non-singulr mtrix This is not utomticlly the cse in: Cut-off of economic flows Multifunctionl unit processes A choice between lterntive processes Closed loop recycling Be creful how you use full LCIs s unit processes/ working together in this clss