Methane from SWDS

New Norwegian calculating model

Per Svardal

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2004 revision of model from 1999

•Many reasons. For reasons and results see www.sft.no/publikasjoner/luft/2079/2079.pdf

•Two of the reasons were:-Complicated model, difficult, poor view of calculations (black box).

-Faulty mathematics.

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Basic mathematics, first order reaction

Rate of reaction equation, reactant transforming to methane:

dDDOC =DDOC * k * e^-kt *dt

Integrated equation for mass calculations, year t:

DDOCdiss = DDOC * (e^-k(t-1) – e^-kt)

(DDOC = dissimilable organic carbon)

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Important theory

•First order reaction-Amount of product formed (DDOCdiss) always proportional to the amount of reactant (DDOC)

-When we know the full amount of DDOC it is of no concern to the calculations when the DDOC came into the SWDS: Every year can be regarded as the first year.

-First order reaction equation the same as the compound interest equation, with negative interest rate.

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Yearly steps in new calculating model

1. Calculate reactant deposited (DDOCd)

2. Add this to the reactant left as not dis-similated from last year (DDOCd+DDOCly)

3. Calculate DDOCdiss from 2.

4. Calculate the amount of methane formed from DDOCdiss.

5. Calculate DDOC not dissimilated for next year’s calculations (new DDOCly).

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The ”motor” of the new model

Two main equations:

DDOCdiss = (DDOCd+DDOCly) * (1-e^-k)

DDOCly = (DDOCd+DDOCly) * e^-k

- (The presented workbook model is a little more complicated because it also handles the option of reaction start in the year of deposition)

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The workbook

•Sheet 3-Parameters

•Sheet 4-Material input and final result

•Sheets 5-7-Calculations for the different materials

•Sheet 8-The accumulation of plastics

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