Thursday, December 29, 2011

2011 Retrospective

This is my 41st and last blog post for 2011.  It’s a good opportunity to review what I have written about and to consider adjustments.  I hope those who visited the blog (3,800 page views in total) have found topics of interest.

An index of postings is provided at the end.  You’ll see that about half the posts relate to the cost of solar power.  This was more or less as anticipated at the start of the year.  I’ll comment further below on my methodology, as well as on the results and lessons I’ve learned.

My research this year remained focussed on evaporation heat engines and condensation heat pumps.  The highlight was the investigation of the Expansion-Cycle Evaporation Turbine [2011-05-12, 2011-05-16, 2011-06-13], which culminated in a substantial paper accepted for the ASME Journal of Engineering for Gas Turbines and Power. 

Despite best efforts, I didn’t get much traction with this idea from the manufacturers of gas turbines, huge companies all of them.  But I persist in the expectation that the concept might find application to provide a power boost at times of peak demand in the electricity grid. 

The ECET work also featured in a paper I presented to the 2011 Conference of the Australian Solar Energy Society [2011-11-12].  That was a comparison of bottoming cycles to boost the power output of solar hybrid gas turbines.

Personally, my biggest learning experience this year was the Fukushima disaster, triggered by the earthquake and tsunami on 11 March.  I had been preparing a post about the cost of nuclear power at the time of the accident, and completed the post on 14 March [2011-03-14], before the full implications of Fukushima were clear.  At the time, my stance was that I was prepared to accept nuclear power in a handful of countries that were technologically advanced and stable enough to manage all the issues, provided the comparative cost of power was assessed in an honest way.  Japan was one of the few countries that I thought would be suitable.

The events at Fukushima made it clear to me that nuclear energy is to be avoided completely.  Human nature simply cannot be trusted where there are commercial incentives to compromise on safety.  If energy technology is local in scale, doesn’t pollute the air and is easily decommissioned, then commercial shortcuts won’t cause a long-term threat to our planet.  But that’s not the case with nuclear – the effects of long-tail (i.e. rare, high damage) accidents might persist for millennia, and that is a risk that I find simply unacceptable.  So I came to the same conclusion as the German government – phase out existing nuclear plants and don’t build any more!

My most viewed posts are “How long until fossil fuels are all used?” and “Atmospheric levels due to fossil fuels” [2011-03-15, 2011-03-20].  On an occasional basis, perhaps in 2012, I’ll provide updates for the first of these.

I investigated CO2 emissions in power generation, particularly how the cost of power would be affected by imposing a social cost on Carbon or a CO2 tax [2011-04-23, 2011-05-16, 2011-06-13, 2011-10-10].  The general conclusion here is that fossil power involves many externalities, which, if properly accounted for, would make coal-fired power much more expensive than it is at present.

I was pleased with two posts unrelated to the mainstream of my work. The first [2011-06-09] investigated the long-term effect of burning one kg of fossil fuel – how much would the CO2 emissions contribute to global warming, and how does that compare to the energy released at the time of combustion?  The second [2011-10-19] looked at issues with CO2 uptake in algal ponds.

At the end of the year, I turned my attention to the condensation heat pump.  I realised that the theoretical Coefficient of Performance, as I defined it, is better than Carnot, so that had to be a blog topic [2011-12-08].  I also investigated the performance of existing condensing heat pump dryers [2011-12-22].  This was an instance in which I have told the truth but not the whole truth, since I also looked at the expected performance of my condensation heat pump in continuous-flow format, as affected by inevitable turbine and compressor losses.  That’s commercially sensitive information, so I won’t give the results at this stage.

What remains is the major thrust of the whole blog – the cost of solar power.  I determined a methodology for cost comparisons and applied it to data I gathered on 16 large-scale solar projects around the world.  My approach was simple but fair.  The Levelised Electricity Cost (LEC) was assessed using the assumptions:
·         there is no inflation,
·         taxation implications are neglected,
·         projects are entirely funded by debt,
·         all projects have the same interest rate (8%) and payback period (25 years), which means that the rate of capital return in 9.4%,
·         all projects have the same annual maintenance and operating costs (3% of the total project cost), and
·         government subsidies are neglected.

Those assumptions are perfectly suitable for comparisons between projects, even if they wouldn’t be suitable for an investment case to financiers.  In retrospect, I now think the maintenance costs are too high, so I’ll reduce the 3% rate to 2% in future.

Below I summarise the results of these investigations.  The first two entries are for my evaporation engine at Wellington in inland New South Wales.  The annual maintenance costs for these are retained at 4% of total project cost.  For all the others, I’ve adjusted the annual maintenance cost to be 2% of total project cost.  The entries with asterisks * are where I had to estimate annual output from claimed CO2 emissions avoided, always a risky process.

On these numbers, my evaporation engine would be highly competitive, world-beating even.  However I’m the first to point out that more work is required to firm up my estimates.

Project
Cost
Cost
Capacity
per peak Watt
per MWhr
Factor %
Wellington
AUD 1.38
AUD 173
13.0
(horizontal)
Wellington
AUD 1.42
AUD 128
17.9
(sloping)
Nyngan*
AUD 3.00
AUD 183
21.3
Olmedilla
EUR 6.40
EUR 503
16.6
Andasol
EUR 6.00
EUR 188
41.0
Greenough
AUD 5.80
AUD 236
32.0
Solar Oasis
AUD 5.75
AUD 397
18.8
Lazio
USD 2.08
USD 163
16.6
Kogan Creek
AUD 2.38
AUD 271
11.4
New Mexico
USD 4.64
USD 228
26.5
Ibersol
EUR 6.00
EUR 200
38.8
Ivanpah
USD 5.56
USD 231
31.5
Stardale
CAD 4.24
CAD 409
13.5
Blythe (first half)
USD 5.79
USD 290
25.9
Solar Dawn
AUD 4.80
AUD 285
21.9
Moree Solar Farm*
AUD 6.15
AUD 263
30.4
Lieberose
EUR 3.03
EUR 350
11.4
Gemasolar
EUR 14.52
EUR 300
63.1

In the coming year, I’ll continue with research on the evaporation heat engine and condensation heat pump.  I’ll also persevere with this blog, again with the prime focus being the cost of solar power.  The price of PV systems fell steeply in 2011, so I expect I’ll observe a significant reduction in the cost of installations.  We’ll see.

I close with an index of my posts for 2011 and my best wishes for 2012.

2011-01-02      Welcome to my new blog
2011-01-07      Cost of solar power – 1
2011-01-11      Cost of solar power – 2
2011-01-22      Research update
2011-01-28      Cost of solar power – 3
2011-02-28      Cost of solar power – 4
2011-03-03      Cost of solar power – 5
2011-03-14      Cost of nuclear power
2011-03-15      How long until fossil fuels are all used?
2011-03-20      Atmospheric CO2 levels due to fossil fuels
2011-03-31      Cost of solar power – 6
2011-04-14      Cost of solar power – 7
2011-04-23      Real cost of coal-fired power
2011-04-27      LEC – the accountant’s view
2011-05-03      Cost of solar power – 8
2011-05-12      Research update – ECET etc
2011-05-16      Cost of power – ECET
2011-05-17      Cost of solar power – 9
2011-05-21      Cost of solar power – 10
2011-06-05      Cost of solar power – 11
2011-06-09      Atmospheric temperature increase due to coal combustion
2011-06-13      Savings in CO2 emissions – ECET
2011-06-15      Cost of solar power – 12
2011-06-20      Cost of solar power – 13
2011-06-21      Cost of solar power – 14
2011-07-01      Cost of solar power – 15
2011-07-02      Cost of solar power – 16
2011-07-16      ECET paper accepted
2011-07-27      Colloquium at UniMelb
2011-08-03      AuSES Sydney talk
2011-08-15      Yet more on LEC
2011-08-22      2011 Solar World Congress
2011-08-25      Blythe switches to PV
2011-09-30      2011 Solar World Congress
2011-10-10      Cost of coal-fired power - more
2011-10-19      CO2 for algal fuels
2011-10-27      Climate Science for Business Champions
2011-11-12      Paper accepted for AuSES
2011-12-08      Beyond-Carnot heat pump?
2011-12-22      Condensing heat pump dryers
2011-12-30      2011 retrospective

Wednesday, December 21, 2011

Condensing heat pump dryers

In my last blog post, I discussed why the Barton Drying Engine has a remarkable Coefficient of Performance as a heat pump.  Moreover the BDE is a drying device as well – it heats and dries the air at the same time.  That leads to a question – how good are existing condensing heat pump dryers?  Perhaps the answer to that question will encourage me to pursue putative financiers with greater gusto.

The answer is now provided …

The figure below is a schematic of a conventional condensing heat pump dryer, such as is now widely available.  In this design, moist air from the tumble dryer is cooled in the evaporator for the refrigerant circuit.  This causes condensation of some water vapour to water, with water removed from the circuit.  The dry cold air is then warmed in the condenser for the refrigerant circuit, before being returned to the tumble dryer where it again picks up moisture.  Two necessary components not depicted in the figure are an inline filter and a blower to keep the air circulating. 
Schematic of a heat pump dryer.  Here black lines indicate airflow, blue lines indicate flow of refrigerant, and the purple squares are heat exchangers (evaporator and condenser for refrigerant).  The X on the refrigerant circuit is a throttling valve that lets condensed high-pressure refrigerant escape to the evaporator.

Palandre & Clodic [1] have experimentally studied the performance of condensing heat pump dryers.  Their paper also includes dryers based on mechanical steam compression, but I won’t discuss that aspect here.

For the conventional dryer studied by P&C, temperatures at the various parts of the circuit are:

drying temperature, Td                   40°C
evaporator temperature, Te            15°C
condenser temperature, Tc             60°C
blowing temperature, Tb                slightly less than Tc

Introduce the notation:

Qe                                heat transfer in evaporator [J_th/sec]
Qc                               heat transfer in condenser [J_th/sec]
W                                work done by compressor in refrigerant circuit [J_e/sec]
W′                               work done by blower and tumble motor [J_e/sec]
COPheating                           Qc / W

global COPheating          Qc / (W+W′)

P&C give the results

COPheating = 3.35 ([1], Table 3),
global COPheating = 2.2 ([1], Figure 13).

From these it follows that

(W+W′) / W = 3.35 / 2.2   which gives   W′/W = 0.52.

P&C Figure 14 gives the total energy consumption of the heat pump dryer as 1,730 Wh = 1730 × 3600 J in 105 × 60 seconds.  It follows that

W+W′ = 1730 × 3600 / (105 × 60) = 989 J /sec.

Then since W′/W = 0.52, the various quantities can be calculated explicitly:
W = 650 J_e/sec,
W′ = 338 J_e/sec,
Qc = 2,179 J_th/sec.

That tells us the nameplate performance of this particular condensing heat pump dryer.  Let’s now interpret the results …


Neglecting heat exchanger losses, heat transfer Qc raises the temperature of the air from Te to Tc, an increase of 45°C.  But note that the overall effect is to raise the air temperature from Td to Tc, an increase of only 20°C from inlet to outlet.  Thus to compare P&C results with my drying engine (BDE), COP_heating  as calculated by P&C needs to be multiplied by 20/45:

(1)        COPheating, comparison = 3.35 × 20/45 ≈ 1.49.

Note also that the comparative global COP would be even lower, namely

(2)        global COPheating, comparison = 2.2 × 20/45 ≈ 0.98.

Heat exchanger inefficiencies are not expected to dramatically alter the above conclusions.  These would mean that the temperature of the air circuit would not reach Te after the evaporator; rather it would be Te + δe.  Nor would the temperature reach Tc after the condenser; rather it would be Tcδc.  Thus the temperature increase over the condenser would be Tcδc – (Te + δe) = TcTe – (δc+ δe).  Equation (1) then would become
(3)        COPheating, comparison = 3.35 × (20 – δc) / (45 – {δc + δe}).

Provided the condenser and evaporator are both reasonably efficient, then estimates (1) and (3) should not differ greatly.

To sum up …

The COP quoted by P&C is as conventionally defined in heat pumps.  However it overstates the actual performance of condensing heat pump drying by a factor of 45/20 = 2.25.  Equation (1) is a better way to assess the heat pump effect for drying.  Once other power requirements are taken into account, equation (2) gives the actual performance that a user would see.

I have compared P&C’s results with my BDE condensation heat pump (in continuous-flow form).  At the present time, the results are a commercial secret.

Acknowledgement

Thanks to Anthony Kitchener for comments on this work and for providing the reference by Palandre & Clodic.

Reference

[1]  L Palandre & D Clodic, “Comparison of heat pump dryer and mechanical steam compression dryer”, International Congress of Refrigeration, Washington, D.C. (2003).

Wednesday, December 7, 2011

Beyond-Carnot heat pump?

Figure 3 below shows a heat pump that has a Coefficient of Performance superior to a Carnot heat pump operating over the same temperature range.  But that contradicts the 2nd Law of Thermodynamics.  How is this paradox to be resolved?

Please read on …

In 2004 I invented a new heat pump which I grandiosely called the Barton Drying Engine (BDE).  This has the following features:


  • Mechanically expand a parcel of moist air; this lowers the temperature of the air as well as the partial pressures and densities of its component gases.
  • Condensation forms immediately when dew point is reached, and any further expansion takes place along a moist adiabat.
  • After the expansion is complete, collect the condensed droplets and remove them from the parcel of air.
  • Re-compress the parcel of air back to ambient pressure; this involves an increase in temperature and partial pressures and densities.  Re-compression takes place along a dry adiabat.  Overall, work must be supplied to complete the cycle.
  • The exhaust stream is hotter and drier than the inlet air stream.


I published a theoretical analysis of the BDE cycle in 2008 [1], with the main assumptions that air and water vapour are ideal gases with constant specific heat capacities.  The principal results are shown in Figure 1 (click to expand).


Figure 1: Results from [1] for the loss-free condensation heat pump.  The inlet air stream is saturated and at the temperature shown.  The results also depend on the expansion ratio.  Clockwise from top left: specific mass change in water vapour during cycle [kg/kg dry air], specific work output per cycle [J/kg dry air], temperature increase from inlet to outlet [°C], COP as a heat pump [dimensionless].

Here the Coefficient of Performance (bottom left diagram in Figure 1) was defined by


COP = ma CaP (T4-T1) / W


in which CaP is the specific heat capacity of dry air at constant pressure, ma is the mass of dry air in the parcel, T4 is the outlet temperature, T1 the inlet temperature and W is the work required to complete the cycle.  In words, the COP is the desired output (heat increase in the parcel of air) divided by the necessary input (work to complete the cycle).

Let’s remind ourselves about Carnot heat pumps, as shown in Figure 2.  This depicts a theoretical heat pump that takes heat energy QL from a reservoir at temperature TL and delivers heat energy QH to a reservoir at temperature TH.  This requires work W.

Figure 2:  Illustrating heat transfer and work requirement of a heat pump.


The COP of the heat pump is COP = QH / W.  But conservation of energy gives QL + W = QH and so

COP = QH / (QH – QL) =   1 / (1 – QL/QH) .

The 2nd Law of Thermodynamics gives that for a reversible process

QL/QH = TL/TH    (temperatures in Kelvin),

so that the COP can be written

COP_Carnot = 1 / (1 – TL/TH) = TH / (TH – TL).

This is the highest COP that a heat pump operating on a closed cycle between TL and TH can have.


Now let’s take the COP shown in Figure 1 (bottom left) for the case when T1 = 25°C and compare it to the Carnot COP (with TL = T1 and TH = T4).  I’ll now also explicitly take account of the water vapour that passes through my heat pump as follows

COP_BDE = { ma CaP + (mv - δmv )CvP } (T4 -T1) / W.

Here mv is the mass of vapour in the parcel of air at the inlet and δmv is the mass of vapour that condenses into water.  CvP is the specific heat capacity of water vapour at constant pressure.  (This expression for COP_BDE gives almost identical results to the previous COP expression used in Figure 1.)

Figure 3 has the results …


Figure 3: Plots of COP_BDE and COP_Carnot for the case when the inlet air is at 25°C and saturated.

But this says COP_BDE is greater than COP_Carnot, which is not possible according to the 2nd Law of Thermodynamics.  I have done similar plots for other saturated inlet conditions, with similar results:  COP_BDE   >  COP_Carnot.  Assuming I haven’t made any numerical mistakes (I have checked very carefully!), and assuming the 2nd Law of Thermodynamics isn’t wrong (it isn’t!), how can this be so?

The paradox is resolved with the aid of Figure 4.


Figure 4: Schematic diagram of the condensation heat pump.

In Figure 4, the BDE is a mechanical device indicated by the yellow box.  It takes in work W and moist air at temperature T1, and gives out condensed water at temperature T3 and drier air at temperature T4.  Let h denote specific enthalpy and subscripts a, v and w denote dry air, water vapour and water respectively.  The change in enthalpy of the water vapour that condenses is

Δ = δmv × { hv(T1) – hw(T3) } = δmv × { hv(T1) – [hv(T3) – L(T3)] }


in which L(T3) is the latent heat at T3, i.e. the specific enthalpy required to evaporate water.  Since we are assuming ideal gas theory with constant specific heats, it follows that


Δ = δmv × { CvP (T1 – T3) + L(T3) }.


Both terms in Δ have the same sign, and Δ is large and positive.

By conservation of energy, if the condensed water loses an amount Δ in enthalpy, then the gaseous components that pass through the heat pump must gain enthalpy (W + Δ).  Therefore the COP of the BDE heat pump is


            COP_BDE  =  (W + Δ) / W  =  1 + (Δ/W).



As an illustrative example, consider the following data from the loss-free computations published in [1]:

inlet temperature:                T1 = 25°C and saturated
lowest temperature:            T3 = 4.9°C
outlet temperature:             T4 = 52.7°C
expansion ratio:                    r = 1.6
water condensed:                 0.01067 kg/kg dry air
work requirement:               W = 1,765 J/kg dry air
latent heat:                             L(T3) = 2,489,600 J/kg water

With the above data, Δ/W evaluates to 15.3, and so COP_BDE is 16.3, which agrees exactly with the results shown in Figure 3 at r = 1.6.  (For the same temperature range,  COP_Carnot  =  (52.7 + 273.15) / (52.7 – 25) = 11.8, also as shown in Figure 3.)

Thus the gas mixture (air plus vapour) that passes through the BDE has an excellent COP, which is sustained by the large loss of enthalpy in the vapour that is condensed. 

Finally, to resolve the paradox in words …

A Carnot heat pump must operate on a closed-loop cycle, with the state of the device at the end of the cycle identical to its state at the beginning.  Also the internal workings of the device must not generate any entropy, so that everything is reversible.

It’s easy to see from Figure 4 that the BDE heat pump does not satisfy this condition, and its COP, as I have defined it, is therefore not subject to the Carnot constraint.  The expansion and compression processes are indeed reversible, but removal of condensate means that the conditions at the end of the cycle are not the same as those at the beginning.

To finish, a brief practical comment.  Theoretically the BDE has great promise.  I am currently evaluating how the performance is affected by inevitable losses in the device.

Reference

[1]  N G Barton, “An evaporation heat engine and condensation heat pump”, ANZIAM Journal, 49 (2008), 503-524.