Biochar has recently received very positive press and is being promoted by several nongovernmental groups. One hears from time to time the claim that “biochar sequesters carbon dioxide,” and this claim requires explanation to the uninitiated, though it is well understood by those who have researched this field^{1}. Woolf et al.^{2} have in fact shown how the sequestration can increase steeply and eventually level off as the benefits saturate in the long term. This paper deals with the sequestration at early times in the process of application of biochar to agriculture. A simple model of the inputs and outputs of carbon dioxide into and from the atmosphere is outlined.

The processes by which biochar gives rise to net sequestration of CO_{2} are the following:

1) The biochar itself is produced by pyrolysis of waste organic matter of almost any kind; 2) the resulting charcoal (biochar) is then put into the ground, preferably with mulch or compost etc., to improve the fertility of the soil; 3) the additional plant growth resulting from the enrichment of the soil gives rise to additional sequestration through photosynthesis, and in general this means better plants and crops as well. There is an annual cycle at work here, at least, in temperate climates so, instead of using differential equations, we can do the arithmetic in one-year steps.

### Single enrichment with biochar

The simplest example is the following. A single batch of biochar is made from a mass of solid organic waste, resulting in approximately T tonnes of biochar and about T tonnes of carbon put back into the atmosphere. [The initial mass of organic waste is greater than 2T tonnes, because the organic waste contains other elements than carbon.] The process of pyrolysis is exothermic, so that the heat generated can be used industrially or domestically. Nevertheless, about T tonnes of carbon are put back into the atmosphere, which is to be recovered through additional photosynthesis in the next years. Suppose now that the T tonnes of biochar are distributed in the top 20 cm of soil at 1 kg/m2, it would enrich T/10 hectares of land. The precise area of land is not important in this analysis; what will turn out to be important is the length of time that is required to sequester the tonnage of carbon equal to the tonnage returned to the atmosphere through pyrolysis. We now assume that the biochar (plus mulch, as appropriate) will increase the photosynthesis on that area by T/x tonnes of growth in the first year. We have thus returned T tonnes of carbon to the atmosphere and reabsorbed T/x additional tonnes by photosynthesis through soil improvement. Provided the soil is kept as fertile from year to year as it was the first year, possibly by adding some more mulch, the same growth (approximately) will be possible in subsequent years as occurred the first year, given adequate rainfall, etc. as is always necessary when we are considering plant growth. This means that in x years, all the initial carbon put back into the atmosphere through pyrolysis has been recovered through photosynthesis. Further enhanced growth in the next few years on that land results in net sequestration (see the numbers in the line for year 1 in Table 1).

This picture is of course highly simplified, and smoothes over the real results for good and bad growing seasons. It also assumes that the effectiveness of the biochar is constant, whereas that property needs to be measured. Does biochar deteriorate with time?

### Multiple enrichments with biochar

To produce those first T tonnes of biochar required a pyrolytic oven, and it would be sensible to use this oven to its capacity every year. The second year’s biochar would be spread similarly on a different acreage, not necessarily adjacent to the first. The soil quality might be different, the crop(s) might be different, and the value of x might be different. Here, however, we shall somewhat oversimplify the picture by adopting an average x-value as being broadly applicable and constant for many years. Table 1 illustrates the result of the first few years of making T tonnes of biochar and spreading it each year throughout an appropriate area. The last line in the table sums the previous lines, to yield the total sequestration over 12 years. Negative values imply that we have put more carbon into the atmosphere than has been sequestered.

**Table 1**

*Sequestration through biochar for x = 4 and successive annual implantation of biochar. All numbers in the table are to be multiplied by T, the tonnage of biochar placed annually in soil. The numbers in each line are those of the line above, shifted one year to the right.*

We see from the sums, last line in Table 1, that a break-even point is only arrived at in year eight, eight being twice the value of x, and net sequestration begins in year nine. A general formula for the net sequestration, S, as a function of x is

S = A + B (y – x + 0.5)2

where y is the year, counting from 0, and

A = – (2x + 1)2/8x and

B = 1/2x

The coefficient B is most important, as it determines the parabolic rise in net sequestration in the long term. The larger B is, the sooner net accumulated sequestration is achieved and the greater that sequestration becomes. For x = 4, as in table 1, at the end of year 12, 12T tonnes of charcoal have been put in the ground, and a net benefit of 6.5T tonnes sequestration has already been achieved. If the planting of charcoal goes on constantly, the total net sequestration follows a parabolic relation, increasing once it has passed the minimum point.

For large values of x, however, the cross-over (or break-even) point at 2x years is so far into the future that it could be irrelevant to addressing climate change in the present, urgent situation. But biochar could still have great benefits for agriculture at high x-values, especially in soils that do not retain water well. There is a remedy for the initial period in which the net sequestration is negative, namely, recovering the effluent gases from pyrolysis. The high carbon dioxide content of the effluent makes it suitable for algae production under controlled conditions, and a great deal is known about useful types of algae that can be produced from carbon dioxide through photosynthesis in water tanks. Recently, there has been mention of “liquid smoke” as a byproduct of emission-free pyrolysis of coconut residues^{3}, though there appears to be little demand yet for liquid smoke.

### Forests

The simplified model above may not apply in the identical arithmetic way to tree growth, but one can safely assume that the maximum increase in photosynthesis will be achieved when the least fertile ground is converted to the most fertile. Afforestation is one of the most important activities that should be embarked upon wherever it makes sense to do it, with or without biochar. But biochar could play a most important role where water retention in the soil is critical.

### Offsets

The arithmetic given here applies, but perhaps only very approximately, to offsets claimed by airlines, such as Air Canada, when they tell passengers that their carbon emissions resulting from flights are offset by tree planting. Since the flights take place daily, and from year to year, no net sequestration fully compensating the emissions, takes place for the first 2x years, where x is the number of years of the per-passenger tree growth required to offset completely one person’s share in the emissions for one flight.

### Conclusions

It is shown here, in a simple model applied to annual crops, that sequestration following the implantation of biochar in soils rises linearly for a one-shot implantation, but quadratically if the implantation is continued annually. Annual biochar implantation doubles the time of onset of net overall sequestration, as compared with the one-shot implantation.

It is important in the context of climate change to apply such biochar where the supplementary sequestration through photosynthesis is maximized, so that the break-even time in sequestration 2x years is as short as possible. Such cases also provide the most sequestration. However, this needs to be done with due regard to biodiversity, and likely requires the avoidance of monocultures. Use of charcoal (biochar) to enhance growth with long break-even times can be useful, but should be accompanied by processing the effluent from pyrolysis to capture the carbon. Such capture of carbon effluent may raise the cost of pyrolysis, but can yield other useful products, and would eliminate the period in which the net sequestration is negative, that is, in which the pyrolysis has caused a net increase in atmospheric CO_{2}.

### Notes

^{1} Dominic Woolf, James Amonette, Alayne Street-Perrot, Joseph Lehmann and Stephen Joseph, “Sustainable Biochar to Mitigate Global Climate Change,” Nature Communications **1** article 56 2010 ^

^{2} *Ibid.* ^

^{3} Oikocredit Info 2010 No.1, p.6 ^