Liquid Air Power Transport Supply Chain The Big Wins Policy Recommendations

Chapter 5: Waste heat

Liquid air is inherently capable of converting waste heat into power because of its low starting temperature. The liquid air cycle works between -200C and ambient temperatures, meaning the addition of even low grade waste of up to 100C, which is otherwise difficult to exploit, can increase the work output significantly. Internal combustion engines produce waste heat at around 100C, raising the prospect of ICE-liquid air heat hybrids, discussed in chapters 4 and 10. Power generation produces high grade waste heat (typically above 400C), and we discuss the potential to integrate this with liquid air concepts in chapter 3 section 3. In this chapter we discuss the potential application of liquid air to plentiful low grade industrial waste heat, and to waste heat from hydrogen fuel cells in transport.

 

There is relatively little publically available data on the surplus heat resource associated with industrial processes in the UK. In its call for evidence on heat in 2008, the Department for Business, Enterprise and Regulatory Reform (BERR) provided an estimate of 40TWh per year¹, but a more detailed bottom up study by McKenna and Norman², which captured an estimated 90% of the energy intensive process industries, put the value at between 10 and 20TWh. It seems safe, therefore, to assume that the true value is in the 10–40TWh range. 40TWh is enough to heat 2.4 million UK homes for one year.³

Nor is there any precise or universally agreed definition of what constitutes ‘low-grade’ heat. BERR categorised high-grade heat as that typically above 400C, medium grade as that between 150–400C and low grade as that below 150C. One justification for this is the distance over which heat can be transported without significant loss: pipeline heat losses typically limit the distances heat can be moved economically to around 5km for steam (at 120C–250C) and a few tens of kilometres for hot water (100C–150C). Crook, on the other hand, defined low-grade heat as that below 250C and this threshold has subsequently been adopted by several workers in the field.⁴ 

McKenna and Norman analysed a range of industries and processes and produced a map showing their distribution (Figure 5.1). Steelworks have a high potential and produce high quality waste heat at three sites in the UK – one in south Wales and two in the north east of England. The other sites and processes with waste heat potential are more widely distributed although there is a distinct concentration in the Midlands, in a band extending from just north of Birmingham to just north of Leeds.

 

Figure 5.1: Map of UK waste heat resource. Source: McKenna and Norman⁵

The range of industries and processes producing waste heat is quite wide, but the form of the resource is less so and a large proportion of it is composed of cooling water streams and flue gases. Therefore existing heat exchanger technology should in principle provide adequate access, although with some caution concerning corrosive or particle laden streams that could lead to damage or fouling of heat exchanger surfaces.

 

When assessing potential uses for waste heat, it is thermodynamically preferable to re-use it as heat rather than convert it into work - for instance as electricity. However, this general rule fails to consider the relative demands for heat and power, or the relative costs of these two forms of energy. For instance, heat may be available but not required, while electricity is very much needed and would otherwise be bought at a high price.

Temperature is synonymous with quality (grade) and can be quantified by calculating the theoretical maximum (Carnot) efficiency of a heat engine operating between the waste heat (source) temperature and the temperature of the surroundings (sink). This value represents the maximum proportion of the waste heat that can be converted to work in a heat engine, and is one measure of the maximum recoverable energy. The Carnot efficiency Ëϲ is given by,

FORMULA

and is plotted in Figure 5.2 as a function of the temperature at which the waste heat is available. In order to generate this figure, the representative average temperature of the surroundings in the UK is assumed to be 10C.

 

Figure 5.2: Theoretical maximum efficiency of waste heat conversion to work, as a function of the temperature of the waste heat

 

On this theoretical basis, and using BERR’s categories, it appears we can recover 58% or more of the high-grade waste heat, 33% to 58% of the medium-grade and up to 33% of the low-grade.

These numbers are certainly overestimates of the true work that can be extracted from waste heat, because:

• they do not account for the fact that heat exchangers require a temperature difference to exist between streams to drive heat transfer, and therefore that the maximum temperature of the working fluid in a heat engine is less than the waste heat source temperature, and the minimum temperature in the cycle is greater than the sink temperature;

• nor do they consider that the source temperature falls as heat is extracted from it to operate the heat engine, and the sink temperature rises as heat is rejected from the heat engine.

The first of these two limitations can be addressed by considering the Novikov and Curzon-Ahlborn efficiencies, which are given by:

FORMULA

and have been shown to be a surprisingly good predictor (±10%) of the actual thermal efficiency of various existing plants. This efficiency is also shown in Figure 5.2 for comparison with the Carnot values. Now our earlier theoretical estimates of the proportion of recoverable waste heat can be revised down to 35% or more for high-grade heat, 18% to 35% for medium-grade, and up to 18% for low-grade.

As for the second limitation, a study by Markides⁶ demonstrates that the decreasing hot temperature and increasing cold temperature always result in a loss of efficiency, but that this should be tolerated to some extent as doing so increases the power output by exploiting more of the available energy per kilogramme of the waste heat stream.

  

If the UK waste heat resource amounts to 10-40TWh, total demand for heat is easily large enough to absorb it. McKenna and Norman assessed the heat demand of UK industry in selected temperature ranges, and Kuder and Blesl⁷ published a similar analysis for Europe. Both identified industries using low-grade heat as pulp and paper, gypsum, food and drink and some chemicals. UK energy intensive industries are estimated to have an overall heat demand of approximately 180TWh with about 25TWh in the less than 100C range and a further 42TWh in the 100–500C range.

The data provided on the previous page suggest demand for low-grade heat in process industries easily matches supply. However, this takes no account of the obvious fact that sources of low-grade heat are rarely co-located and coincident with demand. This suggests the need for a means to store and perhaps transport industrial waste heat.

Where it is not possible to exploit waste heat close to its source, through process integration, another obvious option is to use it for space heating through a district heating network. Such networks are common in parts of Europe and are starting to appear in the UK - in Birmingham city centre for example. However, they typically do not exploit an existing source of waste heat but create a new one – such as a new gas fired generator. Where business or domestic buildings do lie close to waste heat producing industry it is clearly possible to consider district heating. However, the cost of new infrastructure and back-up equipment is likely to be considerable if not prohibitive, meaning technologies that convert waste heat into a more readily useable form of energy may still be preferable.

 

Technologies for harnessing low-grade heat include heat pumps, which upgrade the heat and improve its utility by increasing the options for process integration, and organic Rankine cycle devices, which allow energy from waste heat to be transformed into its most versatile and transportable form – electricity.

There are various types of heat pump. In the domestic arena ground source and air source heat pumps, using an electrically driven vapour compression cycle, extract heat from a very low grade source (the environment) and improve its quality to the point where it can be used for space/comfort heating. They can also be used to provide cooling/air conditioning by rejecting heat to the same environment. Heat pumps operating by the same physical process can also be used in an industrial setting, but the maximum delivery temperature is currently limited to about 120C.⁸ 

The most common heat pumps found in industry are probably mechanical vapour recompression heat pumps. In their simplest ‘open’ form process vapour is compressed and returned with an elevated condensation temperature. In ‘semi-open’ form heat from the recompressed vapour is returned to the process via a heat exchanger. This type of heat pump can achieve high coefficients of performance (COP) of 10–30 and can deliver heat at temperatures of up to 200C.⁹

Chemical and thermochemical heat pumps operating via adsorption or absorption cycles require very little or no electrical power input because the vapour compression process is replaced by a heat driven adsorption/desorption process. The latest generation of such heat pumps can have a delivery temperature of as much as 120C, but COP values are relatively low at 1.2 to 1.4.¹⁰

Overall, heat pumps can provide a very effective way of recovering waste heat, particularly if there is a local need for it as part of a scheme for process integration. Where there is no such need, however, spatial and temporal constraints severely limit this potential. With the possible exception of the mechanical vapour recompression type, heat pumps are not yet widely used for low grade heat recovery and are not yet fully technically mature in this setting.¹¹

 

Most of the world’s electricity is generated by heat engines operating on either the Joule/Brayton or Rankine thermodynamic cycles. The Rankine cycle can operate with water as the working fluid, but this requires high input temperatures such as those produced by coal combustion. When the source is low-grade waste heat, the Rankine cycle needs a working fluid with a lower boiling point. There are a variety of candidates, many of which are organic – hence ‘organic Rankine cycle’ (ORC).

This technology is relatively mature and has been applied with a variety of heat sources including: geothermal, solar, biomass as well as waste heat. ORC equipment is commercially available for waste heat recovery and Tchanche¹² provides 17 examples of installations with capacities ranging from 125kW to 6.5MW.

The biggest advantage of ORC waste heat recovery is that it produces electricity that can be fed into the grid to overcome all spatial and temporal constraints, giving it a commercial value whether or not it can be used within the plant. The main disadvantage is its relatively low efficiency. Large ORC units that use turbo-expanders can be up to 25% efficient, but for smaller units with outputs measured in tens of kW turbo-expanders are not economic. Alternative solutions based on screw expanders are typically less than 10% efficient.

We conclude that even if all process integration opportunities were exploited there would still be a very substantial waste heat resource available from manufacturing and process industries. We also think the best way to access this resource is to generate electricity. In the context of opportunities for waste heat recovery using liquid-air, this suggests the ORC is the main competing technology.

 

ORC machines benefit from relative technical maturity, a growing foothold in the market and from the fact that they are stand-alone units requiring no additional services or inputs. By contrast, any liquid air generator intended to be used for waste heat recovery would need a supply of liquid air or nitrogen. One option would be to install a Cryogenset (chapter 2) and run it on liquid air supplied from a remote, large-scale production facility. The alternative would be to install a full Liquid Air Energy Storage (LAES) unit that produces its own liquid air on site using cheap off-peak electricity. In both cases waste process heat would be used to enhance the recovery of the stored electricity when needed - or when electricity market prices make it economic. In both cases the liquid air acts as a waste heat enhanced energy storage system rather than as a waste heat based generator like the ORC. This suggests that ORC and liquid air are not directly competing technologies. Nevertheless, it is interesting to consider if there is an economic case for the operator of a waste heat generating process plant to purchase a liquid air energy storage set rather than an ORC waste heat generator.

The first law efficiency of liquid air based systems, based on predictions and operational data from the pilot plant (chapter 3, and Appendix 1), are far greater than can be achieved using ORC plant at the same temperatures. The former is predicted to operate at typically 56% whilst the latter operate in the 10-25% range and at the lower end of this range for temperatures around 100C. It therefore seems reasonable to conclude that a liquid air based waste heat recovery system would generate up to five times as much electricity as an ORC system operating under similar conditions with low grade heat. The round trip efficiency of energy storage using liquid air has been estimated to be 50-70%, when enhanced by waste heat. If 50% is assumed for the relatively small scales that would be associated with a process plant, we can compare ORC and liquid air systems for capacity and economics.

If a process plant generates 10MWh of low grade waste heat an ORC set might convert this to 1MWh of electricity to be used on site or sold. A liquid air system would generate 5MWh having previously consumed 10MWh of electricity to generate the liquid air. Given that the power generated can be exported, at a system level the use of liquid air would increase the overall generating capacity at times of peak demand. However, the same effect could be achieved if the liquid air based storage technology were located at existing power stations or industrial gas production sites. The question then is whether the electricity market could provide an economic case for liquid air systems at the sites of industrial process plants.

The levelised cost of electricity (LCOE) generated using ORC has been predicted to be in the range £25-40/MWh (Markides) and it seems reasonable to expect it to be at the high end of this range where low-grade heat is used as the energy source. If we assume that the electricity generated can be sold at £100/MWh then the 10MWh of low grade waste heat would generate a profit of £60.

Using liquid air, the revenue would be £500 and profit would depend of the cost of operating the plant and buying either sufficient liquid air from a centralised generating plant or 10MWh of off-peak electricity to produce the liquid air locally. If non-fuel operating costs - ie operation, maintenance and capital costs - for the liquid air plant were the same as those of the ORC plant and we take these to be £40/10MWh of waste heat used then, to make the same level of profit (£60/10MWh waste heat) the liquid air plant would need to be able to generate or buy its ‘fuel’ for no more than £400, the equivalent of £40/MWh electricity.

This analysis is very simplistic and takes no account of a number of operational and performance factors such as intermittent and part-load performance which could be highly influential. It also excludes an analysis of the relative capital costs, although this is far less influential on the cost of producing liquid air than energy prices (chapter 6). It does, however, identify a key factor in establishing the LCOE with liquid air - the price ratio of peak to off-peak electricity. Whatever other incentives might exist – such as feed-in-tariffs or capacity payments, for example - we have indicated above that if the effective ratio of selling to purchase price is 2.5 or greater¹³, liquid air could represent an economically attractive proposition to process plant operators. 

In countries with inadequate primary generating capacity, such as South Africa and Thailand, the ratio of peak to off-peak electricity prices is as high as eight times even today.¹⁴ In countries or regions with rising renewable generating capacity power prices can already turn negative in periods of high wind and low demand, and the effects of weather and renewable intermittency are expected to increase price volatility in the coming decades. By some analyses the peak to off-peak ratio could rise to well beyond 2.5 times. Figure 5.3 shows projections for price volatility in France and Germany and the effect is expected to be similar in the UK. 

 

Figure 5.3: The impact of renewable intermittency on hourly power pricing. Source: Poyry¹⁵

 

Fuel Cells (FC) are devices that convert chemical energy into electricity with efficiencies typically higher than direct combustion.¹⁶ Depending on the charge carrier and electrolyte, FCs can be further sub-divided into the Proton Exchange Membrane Fuel Cell (PEMFC), Alkaline Fuel Cell (AFC), Phosphoric Acid Fuel Cell (PAFC), Molten Carbonate Fuel Cell (MCFC), Solid Oxide Fuel Cell (SOFC) and Direct Methanol Fuel Cell (DMFC).¹⁷ Of these technologies, PEMFCs are currently receiving most attention in the transport field due to their relatively high power density and quick start-up time.¹⁸

The typical operating temperature of a PEMFC is in the range of 60-80C.¹⁹ Higher operating temperatures can lead to degradation and performance issues arising from the dehydration of the membrane²⁰, while lower temperatures slow the speed of chemical reactions and make water management harder.²¹ The amount of thermal energy removed by the reactant and product streams is typically negligible (1.6%) with most of the heat being removed by the cooling system.²² This is significantly different to an Internal Combustion Engine (ICE) where 60% of the heat is typically removed by the exhaust.²³ Methods of thermally managing PEMFCs include: air cooling, water cooling and cooling using phase change materials.²⁴ The most commonly used cooling method is a mix of deionised water and ethylene glycol combined with a radiator. The high specific heat capacity and sub-zero tolerance make this ideal for automotive applications.²⁵ 

In high pressure FC systems, the thermal management of the compressor and the air is also integrated into the cooling system, due to the heat generated from the compression of the reactant stream.²⁶ It is often preferable to keep the air temperature slightly below that of the stack to avoid condensation, which can cause flooding and loss of performance.²⁷ However, too low an air temperature should also be avoided because it reduces the air’s ability to carry water.

High pressure systems are often preferred in PEMFCs because it makes humidification easier and raises performance due to the increased speed of electrochemical reactions.²⁸ For high pressure systems, positive displacement or centrifugal compressors are preferred.²⁹ Air mass flow rates for an 80kWe stack may typically be in the range of 91 grammes per second with operating pressures in the range of 1.5-2.5 atm and efficiencies of 30-50%.³⁰ Outlet temperatures for air compressors and subsequent heat exchangers can exceed 80C depending on pressure ratios.³¹

 

Any attempt to integrate a liquid air engine with a fuel cell to convert waste heat into power would face three key challenges: space, power blending and thermal management.

Space is always an issue for fuel cells; although the gravimetric energy density of hydrogen is approximately three times that of petrol (120 MJ/kg vs 43 MJ/kg), its volumetric energy density is six times lower (just 4.7 MJ/L at 70 MPa vs 31.7 MJ/L). This means the volume of the fuel tank is an important consideration in any hydrogen application where space is limited such as transport. Any future design for a PEMFC-liquid air hybrid vehicle would need to accommodate the extra space required for a tank of liquid air, although this may be offset by a smaller FC and cooling system.

The power generated by the liquid air engine would need either to be mechanically blended with the electric motor, electrically connected to the drive system BUS via a generator, or stored using an additional energy buffer. Finding the optimum operating points of both the FC and the coupled liquid air engine therefore requires a detailed understanding of the heat generation and temperature dependant behavior of both devices.³² 

The thermal management of both devices therefore becomes a critical consideration in the design of any PEMFC-liquid air hybrid. PEMFCs work best at an operating temperature of approximately 80C. Excessive cooling could result in reduced performance, and could also cause large thermal gradients across the stack which would themselves reduce performance.³³

 

FCs are less efficient when running under dynamic conditions than at steady state; the more transient the load the more inefficient the operation meaning more heat is generated.³⁴ Highly dynamic loads and irregular temperature distributions can lead to faster degradation of PEMFCs.³⁵ A hybrid FC-liquid air engine may allow for greater efficiencies and component lifetime by load levelling of the FC.

Work has already been done to analyse the performance impact of coupling various types of FC and heat engine, and the results show there are significant efficiency gains to be achieved from waste heat recovery.³⁶ This research has mainly focused on higher temperature FCs (usually static), where the temperature gradient between the rejected fluid and the environment is large enough to drive a heat engine. PEMFCs operate at a lower temperatures, so waste heat recovery with heat engines has not been extensively studied. 

The automotive markets where FCs are being considered include buses, where high utilisation, regular routes and centralised refueling address many of the current barriers to mainstream adoption of the technology.³⁷ The size of a bus FC is typically around 250 kWe for a pure FCV and 20-40 kWe for a hybrid FCV.³⁸ For a pure FCV, heat dissipation often requires a sizable radiator and considerable thermal energy is lost. Waste heat recovery would therefore be attractive because of the amount of energy available to be recovered, and because hydrogen’s low volumetric energy density is less significant for buses than for smaller vehicles.

Another vehicle class considered ideal for fuel cells is the taxi, where tighter emissions legislation in urban areas and high utilisation gives the FCV certain advantages over Battery Electric Vehicles (BEV) where a standard eight hour recharge time is desirable.³⁹

One market where fuel cells have already started to be deployed is forklift trucks, where legislation prevents the use of diesel engine vehicles indoors, and again, their high utilisation makes battery electric recharge times problematic.

 

The greatest barriers to mainstream adoption of fuel cells are currently durability and cost.⁴⁰ The most fragile component in a PEMFC is the Membrane Electrode Assembly (MEA), which is required to last 5,000 hours for light-duty vehicles with less than 10% performance decay.⁴¹ Highly dynamic loading of PEMFCs typically accelerates degradation, and research shows this factor accounts for 28% of typical performance fade in transport applications.⁴² As the FC is the most expensive component in the powertrain, maximising the lifetime of this component is important.

One of the main contributors to the cost of a FC is price of the platinum required for its catalyst, estimated at around $48/g in 2010.⁴³ A typical 50kWe FC currently requires 46g of platinum, meaning the catalyst alone will cost $2,240. Manufacturers are targeting major reductions in the amount of platinum used, but this has performance implications. For an 80kWe PEMFC, for example, reducing platinum to around a quarter of current levels would increase heat generation by 50% at peak load and 23% at a continuous load of 61kWe. So the need to cut platinum costs will increase the importance of thermal management in future FC designs and perhaps also the potential value of liquid air technology.

The cost of hydrogen is currently estimated to range from £20/kg to a few hundred £/kg depending on the level of demand and the production method, but the price is forecast to fall to between £4.5/kg to £19/kg.⁴⁴  A PEMFC in automotive applications is approximately five times the cost of its ICE equivalent, with the cost of an ICE being in the region of $25-35/kW.⁴⁵ A hybrid FC-liquid air engine may make the FCV more economical because it would allow the FC and thermal management system to be downsized, and additional electrical energy to be generated from the waste heat recovery.

The opportunities to develop FC-liquid air hybrids, and the potential benefits of doing so, should increase as FCV deployment spreads. The US Federal Transit Administration is providing $16 million under the National Fuel Cell Bus Program to coordinate research amongst manufacturers, engineering firms and transit agencies.⁴⁶ In London, eight FC buses entered operation in 2011 forming Europe’s largest FC bus fleet. London also aims to have at least 65 FC powered vehicles on the road by the end of 2013 including five FC taxis. 

Despite currently high costs of FC systems, carmakers are investing heavily in the development of FCVs. Toyota anticipates the cost of its FCV to fall by 95% from $1 million in 2005 to $50,000 by 2015, when various manufacturers plan to launch FCVs commercially. Other carmakers share a similar outlook, with projected costs of $75,000 in 2015, falling to below $50,000 after five years and an eventual plateau of $30,000 by 2025.⁴⁷ Table 5.1 compares different vehicle platforms.

 

Table 5.1: Comparison of petrol, hydrogen and electrical storage systems in four leading vehicles⁴⁸

PEMFCs are the current technology of choice in the emerging field of FCs for transport applications, based on their relatively fast start-up time and high power density. The main barriers to mainstream adoption are cost and fragility. Most of a PEMFC’s waste heat is dissipated through a cooling loop that operates at approximately 80C. Typically this low grade heat is rejected to the atmosphere through a radiator, since the temperature difference between the fluid and the atmosphere is too small to drive a heat engine. With the development of the liquid air engine there is an opportunity to recover this low grade waste heat to increase FC system efficiency and lifetime, and possibly reduce cost through downsizing. The integration of a PEMFC with a liquid air engine has not yet been studied, and discovering the optimal configuration will require extensive analysis of the temperature dependant performance of both systems.

The markets where a FC-liquid air engine hybrid would offer most immediate benefit and greatest chance of success have been identified as buses, taxis and forklift trucks. These vehicles have a high utilisation and centralised refueling infrastructure, or are used in situations where government legislation creates a supportive context.

 

From the discussion presented above we conclude: 

• The UK industrial waste heat is in the range of 10-40TWh per year. Industrial demand for heat is easily as large, but rarely co-located or coincident with supply, suggesting the need for a means to turn waste heat into a more easily transportable form of energy such as electricity.

• The existing technology for turning waste heat into power, the organic Rankine cycle, is best seen as a baseload generator while liquid air devices act as an energy storage system, so while both exploit waste heat, they are not direct competitors.

• However, based on a comparison with ORC costs, liquid air devices could be economically attractive for waste heat recovery at industrial process sites if the ratio between peak and off-peak electricity prices is 2.5 times or higher. By some forecasts this ratio could be substantially exceeded on a monthly and even daily basis within the next two decades.

• In transport, PEM fuel cells operate at around 80C, not dissimilar to ICE coolant temperatures, meaning they too could be combined into heat hybrids with a Dearman Engine or similar. This could improve the economics of hydrogen vehicles by allowing the PEMFC to be downsized.

• FCs are less efficient when running under dynamic conditions than at steady state, and a hybrid FC-liquid air engine may allow for greater efficiencies and component lifetime by load levelling.

• Manufacturers are constantly trying to reduce the amount of platinum used in fuel cells, but this increases heat generation, meaning thermal management will be increasingly important.

• The markets where a FC-liquid air hybrid would offer most immediate benefit and greatest chance of success have been identified as buses, taxis and forklift trucks.

 

Endnotes 

¹
Heat - Call for Evidence, Department for Business Enterprise and Regulatory Reform (BERR), 2008.

²
Spatial modeling of industrial heat loads and recoverypotentials in the UK, R. C. McKenna et al., Energy Policy 38, 2010, pp5878-5891.

³
The average UK home consumes 16.5MWh of gas per year most of which is used for heating. 40TWh / 16.5MWh = 2.4 million,

⁴
Profiting from low grade heat – The Watt Committee on Energy report No. 26, A. W. Crook, IEEE Energy Series 7, 1993, ISBN 0852968353.

⁵
Spatial modeling of industrial heat loads and recovery potentials in the UK, R. C. McKenna et al., Energy Policy 38, 2010,pp5878-5891, map reproduced with permission from Elsevier.

⁶
The role of pumped and waste heat technologies in a high efficiency sustainable energy future for the UK, C. N. Markides, Applied Thermal Engineering, 2013. In press, available online at http://dx.doi.org/10.1016/j.applthermaleng.2012.02.037.

⁷
Technology orientated analysis of emission reduction potentialsin the industrial sector in the EU-27, R. Kuder et al., International Energy Workshop (IEW), Stockholm, 21-23 June 2010.

⁸
IEA Heat Pump Centre, www. heatpumpcentre.org, accessed January 2013.

⁹
Ibid.

¹⁰
Ibid.

¹¹
A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilization, A. P. Roskilly et al., Applied Thermal Engineering 50,2013, pp1257-1273.

¹²
Low-grade heat conversion into power using organic Rankine cycles – A review of various applications, B. F. Tchanche et al., Renewable and Sustainable Energy Reviews 15, 2011, pp3963-3979.

¹³
The ratio of 2.5 is calculated as follows:

If we assume that the OM costs are the same in both cases and that both plant have access to 10MWh of waste heat then we get the same level of profit if:

 

¹⁴
Tariffs and Charges Booklet 2011/12, Eskom, http://www.eskom.co.za/content/Tariff%20brochure%202011.pdf

¹⁵
The challenges of intermittency in North West European power markets, Pöyry, March 2011, http://www.poyry.com/sites/default/files/imce/files/intermittency_-_march_2011_-_energy.pdf

¹⁶
Fuel Cell Systems Explained, J. Larminie & A. Dicks, Wiley, 2009.

¹⁷
A Review of Polymer Electrolyte Membrane Fuel Cells: Technology, Applications, and Needs on Fundamental Research, Y. Wang et al., Applied Energy 88, 2011, pp981–1007; Comparative study of different fuel cell technologies, S. Mekhilef et al., Renewable and Sustainable Energy Reviews 16, 2012, pp981–989.

¹⁸
Review on fuel cell technologies and power electronic Interface, A. Kirubakaran et al., Renewable and Sustainable Energy Reviews 13, 2009, pp2430–2440; Sustainability study of hydrogen pathways for fuel cell vehicle applications, J-J. Hwang, Renewable and Sustainable Energy Reviews 19, 2013, pp220–229 .

¹⁹
Thermal management issues in a PEMFC stack – A brief review of current status, S. G. Kandlikar et al., Applied Thermal Engineering 29, 2009, pp1276–1280; Thermal and water management of low temperature Proton Exchange MembraneFuel Cell in fork-lift truck power system, E. Hosseinzadeh et al.,Applied Energy 104, 2013, pp434–444.

²⁰
Impedance study of membrane dehydration and compression in proton exchange membrane fuel cells, J-M. Le Canut et al.,  Journal of Power Sources 192, 2009, pp457–466.

²¹
A critical review of cooling techniques in proton exchange membrane fuel cell stacks, G. Zhang et al., International Journal of Hydrogen Energy 37, 2012, pp2412–2429.

²²
Ibid.

²³
Thermal and water management of low temperature Proton Exchange Membrane Fuel Cell in fork-lift truck power system, E. Hosseinzadeh et al., Applied Energy 104, 2013, pp434–444.

²⁴
Thermal analysis and optimization of a portable, edge-air-cooled PEFC stack, R. Flückiger et al., Journal of Power Sources 172, 2007, pp324–333; A numerical study on uniform cooling of  large-scale PEMFCs with different coolant flow field designs, S. M. Baek et al., Applied Thermal Engineering 31, 2011, pp1427–1434; Development of a proton exchange membrane fuel cell cogeneration system, J.J. Hwang et al., Journal of Power Sources 195, 2010, pp2579–2585.

²⁵
A critical review of cooling techniques in proton exchange membrane fuel cell stacks, G. Zhang et al., International Journal of Hydrogen Energy 37, 2012, pp2412–2429.

²⁶
Performance and cost of automotive fuel cell systems with ultra-low platinum loadings, R.K. Ahluwalia et al., Journal of Power Sources 196, 2011, pp4619–4630;  Control-orientated thermal model for proton-exchange membrane fuel cell systems, G. Vasu et al., Journal of Power Sources 183, 2008, pp98–108.

²⁷
Air Management in PEM Fuel Cells: State-of-the-Art and Prospectives, B. B. Lunier et al., 2010, pp1–10.

²⁸
Le Canut, J.-M., Latham, R., Mérida, W. & Harrington, D. a. Impedance study of membrane dehydration and compression in proton exchange membrane fuel cells. Journal of Power Sources 192, 457–466 (2009).

²⁹
Air Management in PEM Fuel Cells: State-of-the-Art and Prospectives, B. B. Lunier et al., 2010, pp1–10.

³⁰
Performance and cost of automotive fuel cell systems with ultra-low platinum loadings, R. K. Ahluwalia et al., Journal of Power Sources 196, 2011, pp4619–4630.

³¹
Yuanyang, Z., Liansheng, L. & Pengcheng, S. Thermodynamic Simulation of Scroll Compressor/Expander Module in Automotive Fuel Cell Engine. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 220, 571–577 (2006).

³²
Modeling and optimization of a typical fuel cell–heat engine hybrid system and its parametric design criteria, Y. Zhao et al.,Journal of Power Sources 186, 2009, pp96–103; Performance analysis and parametric optimum criteria of a class of irreversible fuel cell/heat engine hybrid systems, X. Zhang  et al., International Journal of Hydrogen Energy 35, 2010, pp284–293.

³³
Unsteady 2D PEM fuel cell modeling for a stack emphasizing thermal effects, Y. Shan et al., Journal of Power Sources 165, 2007, pp196–209.

³⁴
Control of fuel cell power systems, J. T. Pukrushpan et al., Springer, 2004; Water and thermal management for Ballard PEM fuel cell stack, X. Yu et al., Journal of Power Sources 147, 2005, pp184–195.

³⁵
Anode and cathode overpotentials and temperature profiles in a PEMFC, O. E. Herrera et al., Journal of Power Sources 198, 2012, pp132–142.

³⁶
Modeling and optimization of a typical fuel cell–heat engine hybrid system and its parametric design criteria, Y. Zhao et al.,Journal of Power Sources 186, 2009, pp96–103; Performance analysis and parametric optimum criteria of a class of irreversible fuel cell/heat engine hybrid systems, X. Zhang et al., Int. J. of Hydrogen Energy 35, 2010, pp284–293.

³⁷
Hydrogen for buses in London: A scenario analysis of changes over time in refuelling infrastructure costs, S. Shayegan et al., International Journal of Hydrogen Energy, 34, 2009, pp8415–8427.

³⁸
Energy system analysis of the fuel cell buses operated in the project: Clean Urban Transport for Europe, M. Saxe et al., Energy 33, 2008, pp689–711; Analysis, operation and maintenance of a fuel cell/battery series-hybrid bus for urban transit applications, P. Bubna et al., Journal of Power Sources 195, 2010, pp3939–3949.

³⁹
Development of integrated fuel cell hybrid power source for electric forklift, T. M. Keränen et al., Journal of Power Sources196, 2011, pp9058–9068.

⁴⁰
A review of polymer electrolyte membrane fuel cells: Technology, applications, and needs on fundamental research, Y. Wang et al., Applied Energy 88, 2011, pp981–1007.

⁴¹
A review of the main parameters influencing long-term performance and durability of PEM fuel cells, W. Schmittinger et al., Journal of Power Sources 180, 2008, pp1–14.

⁴²
Development of Fuel Cell Stack Durability based on Actual Vehicle Test Data : Current Status and Future Work, R. Shimoi et al., SAE International 4970, 2009.

⁴³
The impact of widespread deployment of fuel cell vehicles on platinum demand and price, Y. Sun et al., International Journal of Hydrogen Energy 36, 2011, pp11116–11127.

⁴⁴
Hydrogen for buses in London: A scenario analysis of changes over time in refuelling infrastructure costs, S. Shayegan et al., International Journal of Hydrogen Energy, 34, 2009, pp8415–8427.

⁴⁵
Current status of hybrid, battery and fuel cell electric vehicles: From electrochemistry to market prospects, B. G. Pollet et al., Electrochimica Acta 84, 2012, pp235–249.

⁴⁶
London’s new fuel cell bus fleet unveiled, zero emission route Created, L. Lucas, Fuel Cells Bulletin 2011, pp2–3.

⁴⁷
Current status of hybrid, battery and fuel cell electric vehicles: From electrochemistry to market prospects, B. G. Pollet et al., Electrochimica Acta 84, 2012, pp235–249.

⁴⁸
Ibid.