Tuesday, October 18, 2011

CO2 for algal fuels


I’m grateful to Warren Flentje of the University of Melbourne’s Energy Institute for a recent discussion on issues associated with algal production of biofuels from power station flue gas.  Such biofuels are expected to be economically important in the future, and they also enable re-use of CO2 that would otherwise go directly to the atmosphere in the flue gas.

Algal fuel production can take place in seawater, so water availability is not a show-stopper.  However other major issues to be resolved include
·         the very large amount of hot flue gas to be handled,
·         how to dissolve the CO2 component of this gas in water,
·         the amount of water required, and
·         the energy required to pump the water.

Here, some preliminary estimates are made for how my Evaporation Engine [1] might be of assistance in this process.  With respect to algal fuels, I’m learning on the job; corrections or comments to this post are welcome.

Exhaust gas flow-rate from a 1,000 MW coal-fired power station

·         overall efficiency of the Rankine-cycle steam plant is 33%
·         energy content of coal is 26 MJ/kg
·         Carbon content of coal is 65% by mass
·         coal feed rate is r kg/sec

Considering the energy requirements of the power station, r × 26 ×10^6 = 10^9 / 0.33, so r = 117 kg/sec, comprising 76 kg/sec of Carbon, or 76/0.012 = 6313 moles/sec.

Carbon reacts with air to produce one mole of CO2 from each mole of C, so 6313 moles/sec of O2 are required, which means the O2 mass flow-rate is 6313 × 0.032 = 202 kg/sec. 

Now suppose the inlet air to the power-station is at 300K with ambient pressure 101300 Pa and density 1.176 kg/m^3.  This air contains approximately 21% O2 by volume, so the partial pressure of O2 is 21273 Pa.  At 300K, the ideal gas constant for O2 is 260 J/(kg.K), so the density of O2 in the air is 21273 / (260 × 300) = 0.273 kg/m^3.  If 75% of the O2 is combusted, the required volume flow-rate Fa at the inlet is given by 0.75 × 0.273 × Fa = 202, so that Fa = 987 m^3/s.  The mass flow-rate of air is 987 × 1.176 = 1161 kg/sec.

Algal fuel output

If the power station operates at 100% capacity factor, the amount of Carbon consumed per year is 76 × 3600 × 24 × 365 = 2.40 × 10^9 kg.  If all the Carbon is converted by algal production into fuel with average chemical composition CH2, then the mass of algal fuel is 2.80 billion kg.  At a density of 0.9 kg/litre, that gives 3.11 billion litres, or 19.4 million barrels at 160 litres/barrel.

At USD 100 per barrel, that output is worth USD 19.4 billion, and would be enough to meet the earth’s oil demand for approximately 5.4 hours (at a global consumption rate of 86 million barrels per day).

If the algal fuel system produces 60,000 litres of algal fuel per Hectare per year, the land requirements of the algal system would be 5.18 × 10^4 Ha = 518 km^2.

Power output of the Evaporation Engine

Assume that the hot exhaust from the coal-fired power station is used in the Evaporation Engine [1] to generate power and to cool the air stream. 

Make the following assumptions:
·         coal-fired power station exhaust temperature is 180°C
·         partial pressures of exhaust are Pair = 98.3 kPa, Pvap = 3 kPa; here, it is assumed that CO2 and O2 have similar ideal gas properties for the purposes of operation of the EE, which is an assumption that would need to be modified in a thorough study
·         expansion ratio of the EE is 2.5
·         temperature of injected water is 20°C

Then, from the thermodynamic model for the EE [1],
·         loss-free power output is 24.5 kJ/kg air
·         back-work ratio is approximately 0.8
·         water consumption is 0.046 kg H2O per kg air
·         EE exhaust stream is saturated and at temperature 46°C

After allowing for inevitable engine losses, the power output is estimated at 17 kJ/kg air.  The total power output from the EE would be 1161 kg air/sec ×17 kJ/kg air = 19.7 MW, or 2% of the primary output from the power station.  The water requirement for the EE would be at least 1161 × 0.046 = 53 kg/sec, which, as will now be shown, is only a tiny fraction of the water requirement for dissolving the CO2.

Water requirement to dissolve CO2

The exhaust stream from the EE is transferred at ambient pressure into a closed vessel in which CO2 is dissolved into water.  As assumed earlier, 75% of the O2 in the airstream has been replaced by CO2, which implies the partial pressure of CO2 at the entry to the vessel is approximately 0.15 bar.  (The presence of water vapour in the EE exhaust complicates this estimate and would need to modelled properly in a careful analysis.)

How might the CO2 be dissolved?  I can imagine some sort of a counter-current process, in which the air progressively loses its CO2 component whilst the molarity of the CO2 in the water progressively increases.  The air could be sparged through the water; or perhaps better mass transfer rates could be achieved if small water droplets could be introduced into the vessel.  Whatever, there will be a requirement to pump water around, and that will be estimated in a moment.

First let us calculate the water requirement.  By Henry’s Law (see e.g. [2, p.539]), the amount of CO2 dissolved in water is given by

PCO2 = kH × MCO2

in which PCO2 (bar) is the partial pressure of CO2 above the water, MCO2 is the molarity (moles/litre) of dissolved CO2, and Henry’s constant, kH, actually varies with temperature (i.e. is not a constant).  Using data from [2] and [3], kH is estimated to be 48 bar / {moles CO2/litre} at the exhaust temperature of the Evaporation Engine (46°C).

From Henry’s Law, the molarity of dissolved CO2 will be

MCO2 = PCO2 / kH = 0.15 bar / [48 bar{moles CO2/litre}^-1]  = 0.0031 moles CO2/litre

At this partial pressure for CO2, 1/0.0031 = 323 litres is required to dissolve 1 mole of CO2, and 323 litres/mole × 6313 moles/sec or 2.04 × 10^6 litres/sec of water is required to dissolve the CO2 output from the power station.  This water requirement is nearly 40,000 times that required to operate the EE.

In simpler units, 2040 m^3/sec of water is required to dissolve the CO2 output of the power station.  This very large amount of water needs to be transferred from the sea, then used to dissolve the CO2, then pumped to remote algal ponds, and finally returned to the ocean.

At the very minimum, a head of 5 m water pressure or 50 kPa would be required.  The corresponding power requirement to pump the water is 2040 × 5 × 10^4 = 102 MW, which must be viewed as optimistic.


Let me state the obvious.  Although the estimates presented here are preliminary, they nevertheless highlight difficulties involved in cooling the exhaust stream from a 1000 MW power station exhaust, dissolving the CO2 component in water, and managing water flows through a large expanse of algal ponds.

The EE could certainly be used to cool the coal-fired power station exhaust.  At the same time, the amount of power generated in the EE would contribute towards the power required to transfer CO2 from the EE exhaust stream into water and pump the water around the algal ponds.

A final comment on the Evaporation Engine is pertinent.  If the inlet temperature for the EE is 180°C, the engine could not be operated in continuous-flow mode; rather a piston-in-cylinder mechanism would be required.  The resulting engine that would process all of the power station exhaust would be very bulky, although it should be feasible to construct it at specific capital cost significantly less than $ 1 million/MW.  The thermodynamic cycle of the piston-in-cylinder EE is protected by patent applications, and essential aspects of the mechanical principle to execute the cycle are maintained as commercial secrets.  Introductory details of the EE are available at www.sunoba.com.au.

Thanks to Warren Flentje for drawing this topic to my attention and comments on a preliminary draft.


[1] N G Barton, “An Evaporation Heat Engine and Condensation Heat Pump”, ANZIAM J, Vol 49 (2008), 503-524.
[2] D A McQuarrie & P A Rock, General Chemistry, (Freeman & Co, New York, 1987)
[3] J J Carroll & A E Mather, The System Carbon Dioxide-Water and the Krichevsky-Kasarnovsky Equation ”, Journal of Solution Chemistry, Vol. 21 (1992), 607-621.

1 comment:

  1. The temptation to investigate the use of waste carbon dioxide to produce biomass is inescapable. But is it the best option? Having been involved in the production of betacarotene from Duneliella cells in open brine ponds and running profitable business I think another way. The production of carotenoids is one thing, but there is a need to maximise lipid content for the feedstock for transesterification. That's one point. There is a need to work through strain selection to up the lipid content. There is a need to improve husbandry (pond management)to improve yeilds - that's another.

    However, we do as a nation have very large areas of derelict land that can be used, we have a considerable expertise in our institutions and the algal biotech industry.

    getting price parity with "black" diesel is the goal. Using ponds looks favourable and the algal price is dropping. The use of adjunct technologies such as this evaopration engine in areas of maximal production (sub-tropical) is also favourable.

    Coal (as a combustible resource) may well have a limited future for reasons beyond our control. But is is a source of fine chemicals.