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Background:

For my studies I'm wanting and attempting to make a landfill greenhouse gas emissions (GHG) model that predicts the amount of greenhouse gas equivalent emissions ($GHG_\mathrm{eq}$ [tonnes/year]) by analysing a series of landfill core drill samples and extrapolating the data to predict how much GHGs would be produced if the samples can be representative of the landfill as a whole and allowed to naturally degrade. Note that this comes with the assumption of minimal heterogeneity which I know is not the best assumption for most landfills but I'm hoping to get a LOT of data (it's better than nothing).

As the most notorious GHG from landfill is methane, I'm going to simplify this question to just predicting the amount of methane which would be produced from the (combustible) material in landfill assuming it would just sit there forever.

The Data:

I have this data which is the average of 3 landfill drill core samples and shows the type of waste which has been calculated from sorting and weighing different types of material found in landfill (Table 1) and the chemical composition and high heating value (HHV)/calorific value of the material (Table 2) which I've had tested in an independent lab. For Table 1, an assumed "type" of plastic, rubber, wood (etc.) is made with a constant chemical composition to simplify the model (although I do recognise that there are many different types of plastics and woods etc.).

Data for average of 3 landfill drill core samples

The Method (?):

I've seen the generic methanogenesis combustion reaction as:

$$\ce{CO2 + 4 H2 -> CH4 + 2H2O}$$

I've also seen an elemental formula for hydrocarbon combustions along the lines of:

$$\ce{C_xH_y + {(x + \frac{y}{4})} O2 -> x CO2 + {\frac{y}{2}} H2O + Heat + Light}$$

I know how to calculate the conversion rate going from any GHG such as $\ce{CO2}$ or $\ce{CH4}$ to $GHG_\mathrm{eq}$ but it's this first step - the predicting of the GHGs themselves with what formula - which I'm lost at.

The Questions:

  1. How can I calculate $\ce{CH4}$ from landfill samples with the attached data and which reaction should be used?
  2. (Bonus) What other considerations should be accounted for with any of the other data? (e.g. the Sulfur going into $\ce{SO2}$ emissions (etc.)).
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    $\begingroup$ I am afraid it cannot be easily calculated. AFAIK, landfill methane is formed by microbial activity, which depends on many factors. See also en.wikipedia.org/wiki/Methanogenesis $\endgroup$
    – Poutnik
    Nov 3, 2022 at 5:31
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    $\begingroup$ I assume such models are in large extent empirical. It may be worthy to migrate the question to earthscience.stackexchange.com $\endgroup$
    – Poutnik
    Nov 3, 2022 at 7:38
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    $\begingroup$ This question lies nearer the topic of bioreactor modeling. Others here may be able to help but I have to agree with Poutnik that this might fit better elsewhere, maybe biology SE? $\endgroup$
    – Buck Thorn
    Nov 3, 2022 at 12:16
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    $\begingroup$ Similar comments have been made when I've posted it on other Stack Exchange websites about which site is best. There doesn't seem to be a clear consensus. I'll wait out and hope for an answer in the coming week or so, otherwise I'll put a bounty on it and hope for the best because now I'm very curious and it seems to be a great multidisciplinary challenge. $\endgroup$
    – Hendrix13
    Nov 3, 2022 at 14:53
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    $\begingroup$ Since soil and waste conditions vary, the types of microorganisms vary, as well. For example, what is the moisture level of the site? How large is it? (A deeper dump may have more anaerobic conditions...) Are there specific chemicals present which would encourage or discourage methanogens? Are there methanotrophic bacteria, consuming CH4 as its generated? $\endgroup$ Nov 4, 2022 at 3:32

1 Answer 1

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If you're just trying to get within an order of magnitude or so, here's one approach:

Assume that the landfill is completely sealed, so that no oxygen gas gets in and no hydrogen gas escapes. Also assume that the amount of inorganic redox reactions is negligible (for example sulfate or nitrate reduction).

Now, we'll convert your mass percentages into moles per kg and get:

H = 43 mol/kg

C = 44 mol/kg

N = 00.4 mol/kg

O = 6.6 mol/kg

S = 0.03 mol/kg

Converting this into a crude stoichiometry, we have roughly $\ce{C100H100NO15S_{0.1}}$.

Now we assume that all of oxygen has oxidation state -2, N is -3, S is -2 and H is +1, which is a reasonable assumption for organic matter in the absence of elemental gases. (I'm assuming any hydrogen gas is produced from the organic matter). We then find that that carbon averages an oxidation state of -0.7 per atoms. Assuming that at the end of decomposition, all of the carbon is either methane (oxidation state -4) or carbon dioxide (+4), we would have to have about 60% of the carbon as methane. That would be about 310 g of carbon in the original kg of material ending up as methane, which would have a HHV of about 5500 kcal/kg, not very far off your measured value.

Given that some energy is lost during the conversion of the organic matter to methane (for carbohydrates, this value is about 17 kcal per mole of carbon, so about 550 kcal per kg in our case), the numbers match up surprisingly well.

UPDATE: additional detail on calculations as requested in comments

We assume that the organic material is net neutral and treat the oxidation state as the charge of each atom, which must total up to zero, resulting in the following equation:

$$100*Ox(C) + 100*Ox(H) + Ox(N) + 15*Ox(O) + 0.1*Ox(S) =0$$

Substituting in the assumed values for all but C, we have

$$100*Ox(C) + 100*(+1) + (-3) + 15*(-2) + 0.1*(-2) =0$$ $$Ox(C) = - 0.67$$

I rounded that to -0.7.

Then, to find the ration of methane to CO2, we assume that all of the carbon is one or the other and write the equation for the average oxidation state of carbon atoms:

$$\frac{+4*m_\ce{CO2} -4*m_\ce{CH4}}{m_\ce{CO2} + m_\ce{CH4}}=-0.7$$

Since we're only interested in the ratio $m_\ce{CO2}/m_\ce{CH4}$, we can assign $x$ as the fraction of total C that is methane, so we replace $m_\ce{CH4}$ with $x$ and $m_\ce{CO2}$ with $1-x$:

$$\frac{4*(1-x) -4*x}{1-x+x}=-0.7$$ $$\implies 4-8x=-0.7$$ $$\implies x=0.58$$

which is where I get that about 60% of the carbon is in the form of methane.

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    $\begingroup$ @Hendrix13 - no I actually haven't used either. The hydrocarbon combustion describes burning in air, which is an incinerator not a landfill. The methanogenesis (which isn't a combustion) is just one of many possible final stages of methane production from organic matter, and there are even more ways to convert organic matter initially into substrates for methanogenesis. Luckily for us, the exact pathway doesn't matter. Under anaerobic conditions, they all have to balance out the methane production with CO2 production so that there is no net gain or loss of electrons from the system. $\endgroup$
    – Andrew
    Nov 7, 2022 at 15:26
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    $\begingroup$ The implicit equation that comes from the redox balancing is roughly $\ce{C100H100O15 + 65 H2O -> 60CH4 + 40CO2}$. You can fine-tune the numbers so that it balances properly, but since the calculation is approximate anyway, it doesn't really matter. $\endgroup$
    – Andrew
    Nov 8, 2022 at 13:40
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    $\begingroup$ Microbial decomposition is only going to happen in a wet environment, so I assumed excess water available and that your table was of the dry mass. If there's no water, even the easily degraded material will just sit there. $\endgroup$
    – Andrew
    Nov 9, 2022 at 16:03
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    $\begingroup$ I should have clarified that $m$ here is moles, not mass. it's just a basic calculation of the average redox state of the carbon atoms. $\endgroup$
    – Andrew
    Nov 10, 2022 at 13:15
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    $\begingroup$ The redox balance explains why that stoichiometric balance works, and they're both about the same amount of work. $\endgroup$
    – Andrew
    Nov 12, 2022 at 14:40

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