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Fuel Cell Overall Efficiencies based on Natural Gas
Posted by buddy - Topic Discussions on hydrogen efficiencies

Hydrogen Fuel Cells

 

The maximum efficiency for a hydrogen fuel cell at 25ºC is 83%.  This decreases with temperature, and is 79% at 100ºC.  This maximum efficiency occurs when an infinitesimal amount of work is being done by the cell, or when no load is imposed.  The efficiency under load can be calculated from V, the voltage of an individual cell:

   (1)   EHHV = 100*V/1.481

This equation has been derived from the definition of efficiency, and is based o­n the High Heating Value (HHV) for hydrogen.  Many researchers report efficiencies based o­n the more favorable Low Heating Value (LHV):

   (2)   ELHV = V/1.253

Since there is an exact relationship between the current (I) and the chemical consumption of hydrogen (n gmol/sec), the formulae are a simple o­nes.  Computed values of EHHV and ELHV are chemical/thermodynamic efficiencies and not overall efficiencies.  They do not include leaks, parasitic power or purge.  Overall efficiency must be obtained from actual hydrogen usage and power output.

The voltage of a multi-cell stack is simply the value for a single cell multiplied by the number of cells per stack, so that single cell voltages are easy to obtain.

Efficiencies from single cells with H2 and O2 from bottles usually fit these equations well.  Multi-cell stacks with hydrogen and air under pressure will have more gas leaks, and purge, and must provide power for compression and cooling.

Power output from a cell is:

   (3)   Power out = V*I 

Where I is current in amperes, and power is in watts.  Power output will determine the number of cell stacks to do a job.  Output voltage is tied to cell efficiency, and will determine the cell count per stack to achieve a given voltage.  Most importantly, hydrogen usage, and power loss, will be determined by efficiency.  The table below gives efficiencies based o­n single cell voltage from equations (1) and (2):

SINGLE CELL VOLTAGES

        Voltage                     ELHV                      EHHV

         1.228                                                  83(max)

         1.184                         95(max)            80

         1.00                           80                     68

         0.9                             72                     61

         0.8                             64                     54

         0.7                             56                     47

         0.6                             48                     41

         0.5                             40                     34

The above efficiencies are for any Fuel Cell with hydrogen as fuel.  As discussed, they do not include efficiency loss due to gas leakage, parasitic power, and process purge, which can be quite significant.  In the following analysis it will be assumed that air (21% O2) is used, along with 100% pure hydrogen.

    

 Efficiency and Cell Output

The following table was taken from the literature, for an actual cell stack operating o­n air and hydrogen.  Both were at an inlet pressure of 50 psig.  Hydrogen and air were fed at 1.15x and 2.0x stoichiometric, respectively.  The cell membrane was Nafion 117.

     

EFFICIENCY AND CELL OUTPUT

Single cell       Single              Cell                 Single cell       10 Cells in

Loading           Cell                 Efficiency       Output             Series Output

Amps/sq.ft       Voltage           EHHV                      W/sq.ft             W/sq.ft   

----------------------------------------------------------------------------------

100                  0.88                 59                      88                   880

300                  0.8                   54                    240                 2400

600                  0.68                 46                    408                 4080

900                  0.54                 36                    486                 4860

The area specified in square feet (sq.ft) is the area of o­ne side of the membrane of o­ne cell. Each cell in a stack will pass the same current.  Single cell loading and voltage are measured quantities.  Cell efficiency was calculated from equation (1).  Single cell output is single cell loading multiplied by single cell voltage.

Output for ten cells in series is 10 times the single cell output.  While the loading in Amps/(sq ft) will still be the same for each cell, the overall voltage will increase by a factor of 10.

The table was taken from some good and consistent numbers obtained in 1989, and no doubt there have been improvements since.  The table does illustrate that there is a trade- off between efficiency and output. The fuel cell idles well, but suffers low efficiency at high loading. The efficiencies above do not include parasitic power, purge, or process leaks.  Parasitic power, for higher pressure air in particular, will be high, and purge of hydrogen will be significant for impure hydrogen.

              

High and Low Heating Values

Heating values are based o­n precise chemical reactions.

       For High Heating Value,                  H2 (gas) + 0.5O2 (gas)  >> H2O (liquid)

       For Low Heating Value,                   H2 (gas) + 0.5O2 (gas)  >> H2O (gas).

The difference is H2O liquid >> H2O gas, or the equation for the the heat of vaporization of water.  Heating values can be obtained from common thermodynamic tables.

The generally accepted Fuel Cell maximum efficiency is 83% at 25° C, obtained from thermodynamic properties utilizing HHV. No o­ne has seriously suggested that the maximum is 94.5%, obtained from ΔHLHV and ΔGLHV.  Recall that:

   (4)   Maximum efficiency = Emax = 100*ΔG/ΔH.

Thermodynamic properties for hydrogen are given below:

  

HYDROGEN THERMODYNAMIC PROPERTIES AT 25°C

                                            Corresponding         Corresponding

         Property                      to LHV                    to HHV              Units

        -----------------              ---------------            -----------

        Water Product                 Gas                       Liquid

         ΔH                                 -241,820                -285,830            J/mol

         ΔG                                 -228,570                -237,130            J/mol

         Vmax                             -1.184                    -1.228                 volts

         Emax                              94.5                         83.1                      %

     

An Emax of -1.184V would be generally accepted if it were true, supporting LHV.  But workers have repeatedly found a maximum voltage of near 1.228V in experiments at 25º, and their sensitive equipment can measure thousandths of a volt.

The reactions at the anode and cathode are ionic reactions, again indicating that water must be present, and the product formed as liquid water.  It follows that the product is confirmed as liquid water, so that ΔHHHV should be used, leading to equation (1) above.

          

Process Leaks

Cell design, stack design, membrane material, operating pressure, and other factors will contribute to process leaks.  The effect can be estimated by measuring hydrogen input and power output and computing:

   (5)   Efficiency=100*VI / (n*ΔHHHV)

where n is in moles of hydrogen per second.  This can be compared to the number from equation (1), which incorporates an exact relationship between n and I for chemical conversion o­nly:

   (6)   I/n = 2*F = 2*96,520 coulombs per mole.

In equation 6, F is the Faraday, I is in coulombs/s = amperes, and n in mol/s. Two coulombs are needed for each hydrogen molecule, H2 , thus the 2 in equation (6).

After all of this theory, there is not much else to say about leaks. There will be leaks, as that is the nature of pressure systems, and particularly of hydrogen.

   

Parasitic Power

Because of the relatively low efficiency of the fuel cell stack, provisions have to be made for cooling, necessitating a pump.  Furthermore, as air is used at 40 to 100 psig, there must be an o­nboard compressor.

One manufacturer gives parasitic power losses for a 150 kW plant.  In this plant, air is at 40 psig, and circulation is 2 times stoichiometric.  The gross efficiency has been measured at 48%, but the parasitic power is 39 kW, which gives a net efficiency of o­nly 36%. This is attributed to compression and pumping power o­nly, as the manufacturer uses an ingenious device to recirculate hydrogen, and not a blower.

The computation for parasitic power is not a simple o­ne, as all parasitic power must be generated by the fuel cell. Furthermore, parasitic power is computed from the total energy input which includes parasitic power.

 The compressor power can be computed using equations which give the theoretical adiabatic power required.  One such equation is given in Perry’s Chemical Engineers Handbook, edition 50, equation 6-23e.   Using this equation, the table below was prepared.

    

              POWER FOR COMPRESSION

             For air, with k=1.4.   

                                                Theoretical                  Actual Power

       Outlet Pressure                 Power Required          Required

            psi                                kW/100scfm               kW/100scfm

            10                                 2.7                                4.5

            40                                7.6                               12.7

            75                              11.3                               18.8

          100                              13.3                               22.2

  

The power requirement is directly proportional to the inlet air flow rate, which is measured at 14.7 psi and 32°F.  The inlet pressure is 14.7 psi, or o­ne atmosphere. The actual power is based o­n 60% efficiency for DC to AC conversion, driver, and compressor.  Large compressor sets with large efficient electric motors can have efficiencies in the 70 to 80% range.  Smaller compressors and drivers, and the requirement for variable load, will move efficiency down to about 65%.  A DC to AC conversion efficiency of 92% was used.  Liquid sealed compressor sets will go up to 70% efficiency, but the liquid will end up in the air stream.

     

The pumping requirement is about 120 gallons/minute at 30 feet of head for a fuel cell operating at a chemical efficiency, EHHV = 48%, and input power 412 kW(chemical).  This assumes a 20°F difference between the cooling fluid and the Fuel Cell,. The theoretical power to pump this fluid is 0.65 kW, and for a pump efficiency of 50%, the parasitic power would be 0.65/0.5 = 1.3 kW. This is quite small when compared to the compression power, but high enough to be included.

     

Hydrogen recirculation is necessary to keep a minimum flow through the unit and across the membranes, otherwise impurities can build up.  Hydrogen can be supplied individually to each cell in a stack, but this is impractical.  If hydrogen feeds a series of cells, the first cell will get the highest flow, and the last cell will be dead- ended. Impurities will build up, and cell output will decline, starting with the last cell. Furthermore, cell output is influenced by the flow perpendicular to the cell, which affects the transfer and dissolution of hydrogen.  This mass transfer problem related to hydrogen flow is solved in experimental cells by feeding more hydrogen than is needed, and venting the excess, usually 15%.  This is obviously not a good scheme for a working unit.  In a working cell, recirculation mixes the gas from the last cell with the feed, using an ejector. This ejector is run with hydrogen, which is available at high pressure, so there will be no parasitic power debit.  Impurities are removed by a purge.

     

Hydrogen purge simply removes gaseous impurities which come in with the feed hydrogen. The less pure the feed hydrogen, the more purge.  With 100% hydrogen, there will be no purge requirement.  With <100% hydrogen, the purge will depend o­n the desired hydrogen content of the recirculating gas.  In this analysis it is assumed that H2 recycle is substantial, and all cells in the stack “see” this concentration. This is a conservative assumption.

The table below is based o­n a balance around impurities. 

      PURGE REQUIRED IN % OF FEED

 

     Feed Gas               Hydrogen Content of

    %Hydrogen            Recycle (Circulating) Hydrogen

                                    95         90       80        70

            99.9                 2.0       1.0       0.5       0.3

            99.8                4.0        2.0       1.0       0.7

            99.5              10.0        5.0       2.5       1.7

            99.0                 20        10          5        3.3

            98.0                 40        20        10        6.7

            95                  100        50        25      16.7

     

Very simply, Feed*(impurities in feed) = Purge*(impurities in purge), so that:

          Purge/Feed = (100-Feed H2%) / (100-Recycle H2%)

  

Suppose that the feed is 95% hydrogen, and a minimum of 90% hydrogen is needed at the cells, meaning 90% or less for the recirculating gas.  The purge must be 50% of feed! If 70% hydrogen is circulated, the purge has to be 16.7% of feed.  But the hydrogen content of the recirculating gas is what the cells ‘see’. Lowering the hydrogen content will affect cell productivity and loading.  The solution is to use pure hydrogen! If not, report the purge losses in quoted efficiency.

     

Overall Fuel Cell Efficiency

     

As discussed above, the fuel cell voltage will give cell efficiency. Overall efficiency must include parasitic power and purge. The analysis below illustrates these effects.

All numbers are for 100% hydrogen.

(Single cell LHV efficiency = 57%)

Single cell HHV efficiency= 48%

Total energy input to Fuel Cell System = 418 kW chemical energy

Hydrogen in purge = 16 kW chemical energy (3% purge)

Hydrogen to Fuel Cells = 402 kW chemical energy

Air to Fuel Cells at 2x stoichiometric = 318 cubic feet per minute at 32°F and 1 Atm.

Power to compress air to 50 psig = 43.2 kW

Power to circulate cooling water @120 gallons per minute, and 30 feet of head = 1.3 kW

Fuel Cell outlet power = 402*0.48 = 193.0 kW

Fuel Cell System Net Power out = 193.0-43.2-1.3 = 148.5 kW

Net Fuel Cell System Efficiency = 148.5/(402+16)*100 = 35.5%

This is the true efficiency of the fuel cell system, when all parasitic power and purge are included. There is a huge difference between an advertised LHV efficiency of 57%, and the net fuel cell system efficiency of 35.5% based o­n HHV.

Hydrogen from reforming is at 65% efficiency (HHV) for a medium size plant, giving hydrogen at 350 psig.

For transportation, compression from 350 to 6000 psig will require about 15 kW, or 15/148.5*100 = 10% of outlet power from the fuel cell.

The overall efficiency of Fuel Cell plus transportation is 133.5/418*100 = 32%.

The overall efficiency of Fuel Cell Systems, starting with natural gas at 350 psig, is o­nly 32*65/100 = 20.7%.

Inexpensive internal combustion engines using natural gas can be purchased off the shelf for $~500/kW.  A primary (continuous use) unit @200 kW for $520/kW with efficiency 29% at maximum output, and a cheaper stand-by unit @100 kW with efficiency 23% are offered for sale.  Natural gas turbines (about 400 MW) have efficiencies of about 33%, and combined cycle can go to 55%, for a capital cost of about $450 /kW.  Smaller turbines (80 MW) are at 29% with costs ~$400/kW.  All efficiencies are o­n the same basis, but capital costs include different things for each manufacturer, and are probably plus or minus 20%.  All efficiencies quoted are natural gas to electric power, and no credit is taken for waste heat utilization.

Diesel generators cost about $800/kW for primary machines, and have an efficiency of 40%.  Standby machines are about $200 /kW, with efficiency of ~37%. 

Gasoline powered generators are available in the 1 to 10 kW range, and have efficiencies of ~18% for multi cylinder, four-stroke configuration.  Single cylinder two stroke engines with low compression- ratio for < 1 kW can be lower than 10% efficient  Gasoline powered generators are all standby machines, not intended for more than 10kW or a few days continuous service, and cost from $350 to $650/kW.  Less o­n sale!

The above were all found o­n the internet, except for the large (multi MW) machines, which were from plants in construction, or just started up, in 2001.

The major development problem will be to increase efficiencies while reducing costs by at least an order of magnitude, as fuel cells cost over $10,000/kW.

 



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Very Low Efficiency for Fuel Cells
Posted by buddy - Topic Discussions on hydrogen efficiencies

There is more than o­ne efficiency definition for fuel cells. LHV cell efficiency is based o­n the lower heating value for hydrogen, which increases the published efficiency.  This is an incorret number for fuel cells, and the HHV value should be used. The efficiency for the system of cells must include parasitic power and purge. Finally, if hydrogen is produced from hydrocarbons, the production and transportation efficiencies must be includud. The analysis below illustrates these effects.

All numbers are for 100% hydrogen.

(Single cell LHV efficiency = 57%)

Single cell HHV efficiency= 48%

Total energy input to Fuel Cell System = 418 kW chemical energy

Hydrogen in purge = 16 kW chemical energy (3% purge)

Hydrogen to Fuel Cells = 402 kW chemical energy

Air to Fuel Cells at 2x stoichiometric = 318 cubic feet per minute at 32°F and 1 Atm.

Power to compress air to 50 psig = 43.2 kW

Power to circulate cooling water @120 gallons per minute, and 30 feet of head = 1.3 kW

Fuel Cell outlet power = 402*0.48 = 193.0 kW

Fuel Cell System Net Power out = 193.0-43.2-1.3 = 148.5 kW

Net Fuel Cell System Efficiency = 148.5/(402+16)*100 = 35.5%

This is the true efficiency of the fuel cell system, when all parasitic power and purge are included. There is a huge difference between an advertised LHV efficiency of 57%, and the net fuel cell system efficiency of 35.5% based o­n HHV.

Hydrogen from reforming is at 65% efficiency (HHV) for a medium size plant, giving hydrogen at 350 psig.

For transportation, compression from 350 to 6000 psig will require about 15 kW, or 15/148.5*100 = 10% of outlet power from the fuel cell. (All hydrogen has to be compressed!)

The overall efficiency of Fuel Cell plus transportation is 133.5/418*100 = 32%.

The overall efficiency of Fuel Cell Systems, starting with natural gas at 350 psig, is o­nly 32*65/100 = 20.7%.



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July 13 More on Hydrogen Economy
Posted by buddy - Topic Discussions on hydrogen efficiencies
Question:  But compression seems like a simple thing.  Why are compression energy costs so high?
Simply put, all of the hydrogen fed to the cell has to have been compressed for transport.  The number I give is for a Fuel Cell efficiency of 35.5%.  This is a system efficiency which includes parasitic power.  So lots of hydrogen has to be compressed and transported to feed the Fuel Cell.
Theoretical compression energy can be calculated using standard engineering equations, for example those in "Perry" -Chemical Engineers Handbook,  A compressor efficiency is used to compute actual requirement. 

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July 11, 2005. Hydrogen Economy
Posted by buddy - Topic Discussions on hydrogen efficiencies


Hydrogen Fuel Cells are the projected "backbone" of the Hydrogen Economy.   There are issues in Hydrogen supply, and in the efficiency of Fuel Cells which must be explored.
  I have a page under development to look at Fuel Cell efficiency, and have a hypertext page below for hydrogen production.
If hydrogen is made from natural gas in a medium size facility, the efficiency is o­nly 65%.  Large facilities with higher efficiency are few, and tend to be in remote locations.
Compression of hydrogen from 300 to 6000psi will cost over 10% of the electricity produced by the fuel cell that will use it.  This is the cost of transportation.
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Hydrogen Efficiencies Introduction
Posted by Admin - Topic Discussions on hydrogen efficiencies
Hydrogen System Efficiency

Dr. Barry Pruden, Prodevel Inc.

Introduction:

It has become commonplace to discuss fuel cells and fuel cell systems in connection with environmental protection and methods to eliminate the consumption of fossil fuels. Many scientists bought into the concept of a hydrogen economy several years ago when the focus was on hydrogen production from renewable sources, with hydrogen promoted as the energy carrier of the future.

I have been surprised to see this concept reoriented  to the production of hydrogen from fossil fuels, while retaining the advantages set forth by pioneers for hydrogen from renewable sources.

If hydrogen is to be produced from fossil fuel and used in hydrogen systems, then it must stand on it's own merit in efficiency and cost. As well as compete with fossil fuels on overall environmental and economic impact.

 For example in large plants, the production of hydrogen from natural gas carries a penalty of about 27%. In other words, only 73% of the energy contained in the fossil fuel is now available for use. This production efficiency and the environmental impact of the facility must be included in the evaluation of the overall hydrogen system. Thus if the fuel cells are 40% efficient, and power conditioning is 95% efficient, electricity from fuel cells will be:

(0.73 x 0.40 x 0.95)*100 = 27.7 % efficient and not 40%.



Finally, to maintain a level playing field, all efficiencies  should be based on the high heating value (HHV) of the fuel and products. This can have a significant impact on the reported efficiency. The ratio of HHV to lower heating value (LHV) for hydrogen is about 1.18, so that efficiencies  for fuel cells alone based on LHV will be higher by 18%. When H2O is a product of combustion it can be designated as liquid water, which yields HHV, or water vapor giving LHV. The difference for the specific stoichiometry is the heat of vaporization of water. Hydrogen rich fuels (H2, natural gas) have a high ratio of HHV/LHV.

Why focus on efficiency  if hydrogen is so clean burning and non-polluting?


The answer is that the overall system has to be considered. If the hydrogen system is less efficient than the fossil fuel system then there must be other overriding factors  to promote it. For all systems the natural gas fuel is ultimately converted  to carbon dioxide and water. It follows that the system with the highest efficiency will contribute the least carbon dioxide per unit of electricity. If cleaner cities are desired, then this could be an overriding factor, provided rural areas are willing to accept the environmental cost.  Other pollutants, such as unburned hydrocarbons and oxides of nitrogen will have to be considered in the final analysis.
    
The debate regarding hydrogen as a transportation fuel with onboard reforming is ongoing.


It is difficult to compare the benefits of this system with current technology without some perceived  bias. There is no doubt that current technology is wasteful and non-optimal, but it could be improved given the right incentive. It would, however, be unfair to claim general improvements (smaller, lighter cars with lower payload, no A/C, no power steering or power brakes, and energy saving tires and design) as part of the benefit for hydrogen systems. In addition, the environmental benefit for hydrogen must include the environmental costs of production, as hydrogen is a carrier and not a primary fuel, and the cost for compression or liquefaction, as these are not negligible.
In parallel with the development of hydrogen as a transportation fuel there have been systems developed for the production of electricity by fuel cells. In this case the input is natural gas and the output is electrical power.

 It is the purpose of this paper to compare conventional fossil-fuel systems with fuel cells using integrated reforming for hydrogen generation.


 


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Other Stories
· Fuel Cell Overall Efficiencies based on Natural Gas (Jul 29, 2005)
· Very Low Efficiency for Fuel Cells (Jul 18, 2005)
· July 13 More on Hydrogen Economy (Jul 13, 2005)
· July 11, 2005. Hydrogen Economy (Jul 12, 2005)
· Hydrogen Efficiencies Introduction (Apr 11, 2005)

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